time series work
This commit is contained in:
Jen Looper
Родитель
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Коммит
94339ad9f3
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# Introduction to Time Series Forecasting
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[](https://youtu.be/mAv1SEXUKhE "Introduction to Time Series Forecasting")
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> Introduction to Time Series Forecasting with Francesca Lazzeri; starting at 7:13.
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[](https://youtu.be/wGUV_XqchbE "Introduction to Time Series Forecasting")
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## [Pre-lecture quiz](link-to-quiz-app)
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In this lesson and the following one, you will learn a bit about Time Series Forecasting, an interesting and valuable part of a ML scientist's repertoire that is a bit lesser known than other topics. Time Series Forecasting is a sort of crystal ball: based on past performance of a variable such as price, you can predict its future potential value.
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# [Lesson Topic]
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# Time Series Forecasting with ARIMA
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Add a sketchnote if possible/appropriate
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[](https://youtu.be/IUSk-YDau10 "Introduction to ARIMA")
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> A brief introduction to ARIMA models. The example is done in R, but the concepts are universal.
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## [Pre-lecture quiz](link-to-quiz-app)
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Describe what we will learn
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In the previous lesson, you learned a bit about Time Series Forecasting and loaded a dataset showing the fluctuations of electrical load over a time period. In this lesson, you will discover a specific way to build models with [ARIMA: *A*uto*R*egressive *I*ntegrated *M*oving *A*verage](https://en.wikipedia.org/wiki/Autoregressive_integrated_moving_average). ARIMA models are particularly suited to fit data that shows [non-stationarity](https://en.wikipedia.org/wiki/Stationary_process).
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### Introduction
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> 🎓 Stationarity, from a statistical context, refers to data whose distribution does not change when shifted in time. Non-stationary data, then, shows fluctuations due to trends that must be transformed to be analyzed. Seasonality, for example, can introduce fluctuations in data and can be eliminated by a process of 'seasonal-differencing'.
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Describe what will be covered
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> 🎓 [Differencing](https://en.wikipedia.org/wiki/Autoregressive_integrated_moving_average#Differencing) data, again from a statistical context, refers to the process of transforming non-stationary data to make it stationary by removing its non-constant trend. "Differencing removes the changes in the level of a time series, eliminating trend and seasonality and consequently stabilizing the mean of the time series."[Paper by Shixiong et al](https://arxiv.org/abs/1904.07632)
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> Notes
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Let's unpack the parts of ARIMA to better understand how it helps us model Time Series and help us make predictions against it.
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## AR - for AutoRegressive
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### Prerequisite
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Autoregressive models, as the name implies, look 'back' in time to analyze previous values in your data and make assumptions about them. These previous values are called 'lags'. An example would be data that shows monthly sales of pencils. Each month's sales total would be considered an 'evolving variable' in the dataset. This model is built as the "evolving variable of interest is regressed on its own lagged (i.e., prior) values." [wikipedia](https://en.wikipedia.org/wiki/Autoregressive_integrated_moving_average)
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## I - for Integrated
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What steps should have been covered before this lesson?
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As opposed to the similar 'ARMA' models, the 'I' in ARIMA refers to its *[integrated](https://en.wikipedia.org/wiki/Order_of_integration)* aspect. The data is 'integrated' when differencing steps are applied so as to eliminate non-stationarity.
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## MA - for Moving Average
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The [moving-average](https://en.wikipedia.org/wiki/Moving-average_model) aspect of this model refers to the output variable that is determined by observing the current and past values of lags.
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Bottom line: ARIMA is used to make a model fit the special form of time series data as closely as possible.
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### Preparation
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Preparatory steps to start this lesson
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Open the `/working` folder in this lesson and find the `notebook.ipynb` file. We have already loaded
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---
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# To create the conda environment:
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# $ conda env create -f environment.yaml
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#
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# To update the conda environment:
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# $ conda env update -f environment.yaml
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#
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# To register the conda environment in Jupyter:
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# $ conda activate dlts
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# $ python -m ipykernel install --user --name dlts --display-name "Python (dlts)"
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name: dlts
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channels:
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- defaults
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dependencies:
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- python==3.6.6
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- pip>=19.1.1
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- ipykernel>=4.6.1
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- jupyter>=1.0.0
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- matplotlib==3.0.0
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- numpy==1.16.2
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- pandas==0.23.4
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- tensorflow==1.12.0
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- keras==2.2.4
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- scikit-learn==0.20.3
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- statsmodels==0.9.0
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- xlrd >= 1.0.0
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- pip:
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- pyramid-arima==0.8.1
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import zipfile
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import os
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import sys
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import pandas as pd
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# This function unzips the GEFCom2014 data zip file and extracts the 'extended'
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# load forecasting competition data. Data is saved in energy.csv
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def extract_data(data_dir):
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GEFCom_dir = os.path.join(data_dir, 'GEFCom2014', 'GEFCom2014 Data')
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GEFCom_zipfile = os.path.join(data_dir, 'GEFCom2014.zip')
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if not os.path.exists(GEFCom_zipfile):
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sys.exit("Download GEFCom2014.zip from https://www.dropbox.com/s/pqenrr2mcvl0hk9/GEFCom2014.zip?dl=0 and save it to the '{}' directory.".format(data_dir))
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# unzip root directory
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zip_ref = zipfile.ZipFile(GEFCom_zipfile, 'r')
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zip_ref.extractall(os.path.join(data_dir, 'GEFCom2014'))
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zip_ref.close()
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# extract the extended competition data
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zip_ref = zipfile.ZipFile(os.path.join(GEFCom_dir, 'GEFCom2014-E_V2.zip'), 'r')
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zip_ref.extractall(os.path.join(data_dir, 'GEFCom2014-E'))
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zip_ref.close()
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# load the data from Excel file
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data = pd.read_excel(os.path.join(data_dir, 'GEFCom2014-E', 'GEFCom2014-E.xlsx'), parse_date='Date')
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# create timestamp variable from Date and Hour
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data['timestamp'] = data['Date'].add(pd.to_timedelta(data.Hour - 1, unit='h'))
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data = data[['timestamp', 'load', 'T']]
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data = data.rename(columns={'T':'temp'})
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# remove time period with no load data
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data = data[data.timestamp >= '2012-01-01']
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# save to csv
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data.to_csv(os.path.join(data_dir, 'energy.csv'), index=False)
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import numpy as np
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import pandas as pd
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import os
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from collections import UserDict
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def load_data(data_dir):
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"""Load the GEFCom 2014 energy load data"""
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energy = pd.read_csv(os.path.join(data_dir, 'energy.csv'), parse_dates=['timestamp'])
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# Reindex the dataframe such that the dataframe has a record for every time point
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# between the minimum and maximum timestamp in the time series. This helps to
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# identify missing time periods in the data (there are none in this dataset).
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energy.index = energy['timestamp']
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energy = energy.reindex(pd.date_range(min(energy['timestamp']),
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max(energy['timestamp']),
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freq='H'))
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energy = energy.drop('timestamp', axis=1)
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return energy
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def mape(predictions, actuals):
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"""Mean absolute percentage error"""
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return ((predictions - actuals).abs() / actuals).mean()
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def create_evaluation_df(predictions, test_inputs, H, scaler):
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"""Create a data frame for easy evaluation"""
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eval_df = pd.DataFrame(predictions, columns=['t+'+str(t) for t in range(1, H+1)])
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eval_df['timestamp'] = test_inputs.dataframe.index
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eval_df = pd.melt(eval_df, id_vars='timestamp', value_name='prediction', var_name='h')
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eval_df['actual'] = np.transpose(test_inputs['target']).ravel()
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eval_df[['prediction', 'actual']] = scaler.inverse_transform(eval_df[['prediction', 'actual']])
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return eval_df
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class TimeSeriesTensor(UserDict):
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"""A dictionary of tensors for input into the RNN model.
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Use this class to:
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1. Shift the values of the time series to create a Pandas dataframe containing all the data
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for a single training example
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2. Discard any samples with missing values
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3. Transform this Pandas dataframe into a numpy array of shape
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(samples, time steps, features) for input into Keras
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The class takes the following parameters:
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- **dataset**: original time series
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- **target** name of the target column
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- **H**: the forecast horizon
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- **tensor_structures**: a dictionary discribing the tensor structure of the form
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{ 'tensor_name' : (range(max_backward_shift, max_forward_shift), [feature, feature, ...] ) }
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if features are non-sequential and should not be shifted, use the form
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{ 'tensor_name' : (None, [feature, feature, ...])}
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- **freq**: time series frequency (default 'H' - hourly)
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- **drop_incomplete**: (Boolean) whether to drop incomplete samples (default True)
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"""
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def __init__(self, dataset, target, H, tensor_structure, freq='H', drop_incomplete=True):
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self.dataset = dataset
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self.target = target
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self.tensor_structure = tensor_structure
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self.tensor_names = list(tensor_structure.keys())
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self.dataframe = self._shift_data(H, freq, drop_incomplete)
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self.data = self._df2tensors(self.dataframe)
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def _shift_data(self, H, freq, drop_incomplete):
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# Use the tensor_structures definitions to shift the features in the original dataset.
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# The result is a Pandas dataframe with multi-index columns in the hierarchy
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# tensor - the name of the input tensor
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# feature - the input feature to be shifted
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# time step - the time step for the RNN in which the data is input. These labels
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# are centred on time t. the forecast creation time
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df = self.dataset.copy()
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idx_tuples = []
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for t in range(1, H+1):
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df['t+'+str(t)] = df[self.target].shift(t*-1, freq=freq)
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idx_tuples.append(('target', 'y', 't+'+str(t)))
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for name, structure in self.tensor_structure.items():
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rng = structure[0]
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dataset_cols = structure[1]
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for col in dataset_cols:
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# do not shift non-sequential 'static' features
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if rng is None:
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df['context_'+col] = df[col]
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idx_tuples.append((name, col, 'static'))
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else:
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for t in rng:
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sign = '+' if t > 0 else ''
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shift = str(t) if t != 0 else ''
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period = 't'+sign+shift
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shifted_col = name+'_'+col+'_'+period
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df[shifted_col] = df[col].shift(t*-1, freq=freq)
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idx_tuples.append((name, col, period))
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df = df.drop(self.dataset.columns, axis=1)
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idx = pd.MultiIndex.from_tuples(idx_tuples, names=['tensor', 'feature', 'time step'])
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df.columns = idx
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if drop_incomplete:
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df = df.dropna(how='any')
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return df
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def _df2tensors(self, dataframe):
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# Transform the shifted Pandas dataframe into the multidimensional numpy arrays. These
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# arrays can be used to input into the keras model and can be accessed by tensor name.
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# For example, for a TimeSeriesTensor object named "model_inputs" and a tensor named
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# "target", the input tensor can be acccessed with model_inputs['target']
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inputs = {}
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y = dataframe['target']
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y = y.as_matrix()
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inputs['target'] = y
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for name, structure in self.tensor_structure.items():
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rng = structure[0]
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cols = structure[1]
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tensor = dataframe[name][cols].as_matrix()
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if rng is None:
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tensor = tensor.reshape(tensor.shape[0], len(cols))
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else:
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tensor = tensor.reshape(tensor.shape[0], len(cols), len(rng))
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tensor = np.transpose(tensor, axes=[0, 2, 1])
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inputs[name] = tensor
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return inputs
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def subset_data(self, new_dataframe):
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# Use this function to recreate the input tensors if the shifted dataframe
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# has been filtered.
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self.dataframe = new_dataframe
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self.data = self._df2tensors(self.dataframe)
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Загрузить разницу
Различия файлов скрыты, потому что одна или несколько строк слишком длинны
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@ -0,0 +1,28 @@
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# To create the conda environment:
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# $ conda env create -f environment.yaml
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#
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# To update the conda environment:
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# $ conda env update -f environment.yaml
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#
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# To register the conda environment in Jupyter:
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# $ conda activate dlts
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# $ python -m ipykernel install --user --name dlts --display-name "Python (dlts)"
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name: dlts
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channels:
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- defaults
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dependencies:
|
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- python==3.6.6
|
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- pip>=19.1.1
|
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- ipykernel>=4.6.1
|
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- jupyter>=1.0.0
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- matplotlib==3.0.0
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- numpy==1.16.2
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- pandas==0.23.4
|
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- tensorflow==1.12.0
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- keras==2.2.4
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- scikit-learn==0.20.3
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- statsmodels==0.9.0
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- xlrd >= 1.0.0
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- pip:
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- pyramid-arima==0.8.1
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@ -0,0 +1,37 @@
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import zipfile
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import os
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import sys
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import pandas as pd
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# This function unzips the GEFCom2014 data zip file and extracts the 'extended'
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# load forecasting competition data. Data is saved in energy.csv
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def extract_data(data_dir):
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GEFCom_dir = os.path.join(data_dir, 'GEFCom2014', 'GEFCom2014 Data')
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GEFCom_zipfile = os.path.join(data_dir, 'GEFCom2014.zip')
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if not os.path.exists(GEFCom_zipfile):
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sys.exit("Download GEFCom2014.zip from https://www.dropbox.com/s/pqenrr2mcvl0hk9/GEFCom2014.zip?dl=0 and save it to the '{}' directory.".format(data_dir))
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# unzip root directory
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zip_ref = zipfile.ZipFile(GEFCom_zipfile, 'r')
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zip_ref.extractall(os.path.join(data_dir, 'GEFCom2014'))
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zip_ref.close()
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# extract the extended competition data
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zip_ref = zipfile.ZipFile(os.path.join(GEFCom_dir, 'GEFCom2014-E_V2.zip'), 'r')
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zip_ref.extractall(os.path.join(data_dir, 'GEFCom2014-E'))
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zip_ref.close()
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# load the data from Excel file
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data = pd.read_excel(os.path.join(data_dir, 'GEFCom2014-E', 'GEFCom2014-E.xlsx'), parse_date='Date')
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# create timestamp variable from Date and Hour
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data['timestamp'] = data['Date'].add(pd.to_timedelta(data.Hour - 1, unit='h'))
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data = data[['timestamp', 'load', 'T']]
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data = data.rename(columns={'T':'temp'})
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# remove time period with no load data
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data = data[data.timestamp >= '2012-01-01']
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# save to csv
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data.to_csv(os.path.join(data_dir, 'energy.csv'), index=False)
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@ -0,0 +1,145 @@
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import numpy as np
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import pandas as pd
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import os
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from collections import UserDict
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def load_data(data_dir):
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"""Load the GEFCom 2014 energy load data"""
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energy = pd.read_csv(os.path.join(data_dir, 'energy.csv'), parse_dates=['timestamp'])
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# Reindex the dataframe such that the dataframe has a record for every time point
|
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# between the minimum and maximum timestamp in the time series. This helps to
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# identify missing time periods in the data (there are none in this dataset).
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energy.index = energy['timestamp']
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energy = energy.reindex(pd.date_range(min(energy['timestamp']),
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max(energy['timestamp']),
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freq='H'))
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energy = energy.drop('timestamp', axis=1)
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return energy
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def mape(predictions, actuals):
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"""Mean absolute percentage error"""
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return ((predictions - actuals).abs() / actuals).mean()
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def create_evaluation_df(predictions, test_inputs, H, scaler):
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"""Create a data frame for easy evaluation"""
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eval_df = pd.DataFrame(predictions, columns=['t+'+str(t) for t in range(1, H+1)])
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eval_df['timestamp'] = test_inputs.dataframe.index
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eval_df = pd.melt(eval_df, id_vars='timestamp', value_name='prediction', var_name='h')
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eval_df['actual'] = np.transpose(test_inputs['target']).ravel()
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eval_df[['prediction', 'actual']] = scaler.inverse_transform(eval_df[['prediction', 'actual']])
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return eval_df
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class TimeSeriesTensor(UserDict):
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"""A dictionary of tensors for input into the RNN model.
|
||||
|
||||
Use this class to:
|
||||
1. Shift the values of the time series to create a Pandas dataframe containing all the data
|
||||
for a single training example
|
||||
2. Discard any samples with missing values
|
||||
3. Transform this Pandas dataframe into a numpy array of shape
|
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(samples, time steps, features) for input into Keras
|
||||
|
||||
The class takes the following parameters:
|
||||
- **dataset**: original time series
|
||||
- **target** name of the target column
|
||||
- **H**: the forecast horizon
|
||||
- **tensor_structures**: a dictionary discribing the tensor structure of the form
|
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{ 'tensor_name' : (range(max_backward_shift, max_forward_shift), [feature, feature, ...] ) }
|
||||
if features are non-sequential and should not be shifted, use the form
|
||||
{ 'tensor_name' : (None, [feature, feature, ...])}
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- **freq**: time series frequency (default 'H' - hourly)
|
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- **drop_incomplete**: (Boolean) whether to drop incomplete samples (default True)
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"""
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def __init__(self, dataset, target, H, tensor_structure, freq='H', drop_incomplete=True):
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self.dataset = dataset
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self.target = target
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self.tensor_structure = tensor_structure
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||||
self.tensor_names = list(tensor_structure.keys())
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||||
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||||
self.dataframe = self._shift_data(H, freq, drop_incomplete)
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self.data = self._df2tensors(self.dataframe)
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||||
|
||||
def _shift_data(self, H, freq, drop_incomplete):
|
||||
|
||||
# Use the tensor_structures definitions to shift the features in the original dataset.
|
||||
# The result is a Pandas dataframe with multi-index columns in the hierarchy
|
||||
# tensor - the name of the input tensor
|
||||
# feature - the input feature to be shifted
|
||||
# time step - the time step for the RNN in which the data is input. These labels
|
||||
# are centred on time t. the forecast creation time
|
||||
df = self.dataset.copy()
|
||||
|
||||
idx_tuples = []
|
||||
for t in range(1, H+1):
|
||||
df['t+'+str(t)] = df[self.target].shift(t*-1, freq=freq)
|
||||
idx_tuples.append(('target', 'y', 't+'+str(t)))
|
||||
|
||||
for name, structure in self.tensor_structure.items():
|
||||
rng = structure[0]
|
||||
dataset_cols = structure[1]
|
||||
|
||||
for col in dataset_cols:
|
||||
|
||||
# do not shift non-sequential 'static' features
|
||||
if rng is None:
|
||||
df['context_'+col] = df[col]
|
||||
idx_tuples.append((name, col, 'static'))
|
||||
|
||||
else:
|
||||
for t in rng:
|
||||
sign = '+' if t > 0 else ''
|
||||
shift = str(t) if t != 0 else ''
|
||||
period = 't'+sign+shift
|
||||
shifted_col = name+'_'+col+'_'+period
|
||||
df[shifted_col] = df[col].shift(t*-1, freq=freq)
|
||||
idx_tuples.append((name, col, period))
|
||||
|
||||
df = df.drop(self.dataset.columns, axis=1)
|
||||
idx = pd.MultiIndex.from_tuples(idx_tuples, names=['tensor', 'feature', 'time step'])
|
||||
df.columns = idx
|
||||
|
||||
if drop_incomplete:
|
||||
df = df.dropna(how='any')
|
||||
|
||||
return df
|
||||
|
||||
def _df2tensors(self, dataframe):
|
||||
|
||||
# Transform the shifted Pandas dataframe into the multidimensional numpy arrays. These
|
||||
# arrays can be used to input into the keras model and can be accessed by tensor name.
|
||||
# For example, for a TimeSeriesTensor object named "model_inputs" and a tensor named
|
||||
# "target", the input tensor can be acccessed with model_inputs['target']
|
||||
|
||||
inputs = {}
|
||||
y = dataframe['target']
|
||||
y = y.as_matrix()
|
||||
inputs['target'] = y
|
||||
|
||||
for name, structure in self.tensor_structure.items():
|
||||
rng = structure[0]
|
||||
cols = structure[1]
|
||||
tensor = dataframe[name][cols].as_matrix()
|
||||
if rng is None:
|
||||
tensor = tensor.reshape(tensor.shape[0], len(cols))
|
||||
else:
|
||||
tensor = tensor.reshape(tensor.shape[0], len(cols), len(rng))
|
||||
tensor = np.transpose(tensor, axes=[0, 2, 1])
|
||||
inputs[name] = tensor
|
||||
|
||||
return inputs
|
||||
|
||||
def subset_data(self, new_dataframe):
|
||||
|
||||
# Use this function to recreate the input tensors if the shifted dataframe
|
||||
# has been filtered.
|
||||
|
||||
self.dataframe = new_dataframe
|
||||
self.data = self._df2tensors(self.dataframe)
|
||||
Разница между файлами не показана из-за своего большого размера
Загрузить разницу
|
|
@ -0,0 +1,49 @@
|
|||
{
|
||||
"metadata": {
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": 3
|
||||
},
|
||||
"orig_nbformat": 2
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 2,
|
||||
"cells": [
|
||||
{
|
||||
"source": [
|
||||
"# Time series forecasting with ARIMA\n",
|
||||
"\n",
|
||||
"In this notebook, we demonstrate how to:\n",
|
||||
"- prepare time series data for training an ARIMA time series forecasting model\n",
|
||||
"- implement a simple ARIMA model to forecast the next HORIZON steps ahead (time *t+1* through *t+HORIZON*) in the time series\n",
|
||||
"- evaluate the model \n",
|
||||
"\n",
|
||||
"\n",
|
||||
"The data in this example is taken from the GEFCom2014 forecasting competition<sup>1</sup>. It consists of 3 years of hourly electricity load and temperature values between 2012 and 2014. The task is to forecast future values of electricity load. In this example, we show how to forecast one time step ahead, using historical load data only.\n",
|
||||
"\n",
|
||||
"<sup>1</sup>Tao Hong, Pierre Pinson, Shu Fan, Hamidreza Zareipour, Alberto Troccoli and Rob J. Hyndman, \"Probabilistic energy forecasting: Global Energy Forecasting Competition 2014 and beyond\", International Journal of Forecasting, vol.32, no.3, pp 896-913, July-September, 2016."
|
||||
],
|
||||
"cell_type": "code",
|
||||
"metadata": {},
|
||||
"execution_count": null,
|
||||
"outputs": []
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"pip install statsmodels"
|
||||
]
|
||||
}
|
||||
]
|
||||
}
|
||||
Загрузка…
Ссылка в новой задаче