{"id":199601,"date":"2023-12-01T11:06:48","date_gmt":"2023-12-01T16:06:48","guid":{"rendered":"https:\/\/ibkrcampus.com\/?p=199601"},"modified":"2023-12-01T11:07:07","modified_gmt":"2023-12-01T16:07:07","slug":"python-constructing-time-series-sequence-samples-dataset","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/python-constructing-time-series-sequence-samples-dataset\/","title":{"rendered":"Python: Constructing Time Series Sequence Samples Dataset"},"content":{"rendered":"\n

This post constructs the multivariate time series data into sequence samples dataset for RNNs, LSTMs, CNNs, and similar models in Keras or Tensorflow.<\/p>\n\n\n\n

Time Series Sequence Samples Dataset<\/h3>\n\n\n\n

Sequence-based models such as LSTM require the 3D dataset structure: (batch, timesteps, features). The term ‘batch’ specifically indicates the subset of samples included in a mini-batch during model training.<\/p>\n\n\n\n

Timesteps denote the historical sequence of data instances or temporal lags. Incorporating this temporal dimension (timesteps) constructs a three-dimensional dataset, enabling the effective capture of the data’s sequential nature.<\/p>\n\n\n\n

Python code<\/h3>\n\n\n\n

I’ve made a general function for this purpose:<\/p>\n\n\n\n

f_make_seq_data_from_matrix(data, ts_list, fh_list) <\/strong>.<\/p>\n\n\n\n

The ‘data<\/strong>‘ is a numpy matrix which contains a multivariate time series. ‘ts_list<\/strong>‘ is a list of timesteps, which doesn’t have to be consecutive. On the other hand, ‘fh_list<\/strong>‘ refers to a list of forecasting horizons, capable of representing single or multi-step forecasts and also need not be consecutive.<\/p>\n\n\n\n

This function, such as it is, is capable of handling distributed lags, as well as one-step or multi-step forecasting, and thus, I believe it is helpful for general purposes.<\/p>\n\n\n\n

import numpy as np\n \ndef f_make_seq_data_from_matrix(data, ts_list, fh_list):\n    co_list = ts_list+fh_list\n    coseq_range = range(min(co_list),max(co_list)+1)\n    tsseq_range = range(min(ts_list),max(ts_list)+1)\n    fhseq_range = range(min(fh_list),max(fh_list)+1)\n    tssel_list = [i - min(ts_list) for i in ts_list]\n    fhsel_list = [i - min(fh_list) for i in fh_list]\n    \n    is_seq = []; ot_seq = []; obs = data.shape[0]\n    for i in range(obs - len(coseq_range) + 1):\n        dal = data[i:i + len(coseq_range)]\n        din = dal[:len(tsseq_range)]\n        dot = dal[-len(fhseq_range):]\n        is_seq.append(din[tssel_list])\n        ot_seq.append(dot[fhsel_list])\n    return np.array(is_seq), np.array(ot_seq)<\/pre>\n\n\n\n
The elements of two lists are determined based on the time ‘t<\/strong>‘. For example, -2, -1, 0, 1, 2<\/strong><\/em> correspond to t-2, t-1, t, t+1, t+2<\/strong><\/em> respectively.<\/p>\n\n\n\n
Case 1: Forecasting time t+1 utilizing information from time t<\/strong><\/p>\n\n\n\n
This resembles a typical example, akin to an AR(1) model. Achieving the same result is possible by using ts_list = [-1] and fh_list = [0] since the time lag structure remains consistent.<\/p>\n\n\n\n
# Suppose data has 10 observations with 3 features\ndata = np.random.rand(10, 3)\n \n# Generate suitable sequences for CNN, RNN, LSTM, and so on\nts_list = [0] # selected timesteps\nfh_list = [1] # selected forecasting horizons\n \n# generate sequences dataset for Keras\nX, Y = f_make_seq_data_from_matrix(data, ts_list, fh_list)\n \nprint(\"\\nTimesteps:\", ts_list, \", forecast horizons:\", fh_list)\nprint(\"\\nData\\n\", data, \"\\n Shape of data:\", data.shape)\nprint(\"\\nX\\n\", X, \"\\n Shape of X:\", X.shape)\nprint(\"\\nY\\n\", Y, \"\\n Shape of Y:\", Y.shape)<\/pre>\n\n\n\n
Timesteps: [0] , forecast horizons: [1]\n \nData\n [[0.58708034 0.88707951 0.25878656]\n [0.52696273 0.13857786 0.50993527]\n [0.53533872 0.45365456 0.89658186]\n [0.54978604 0.91198371 0.25040483]\n [0.36520302 0.76098129 0.5341683 ]\n [0.46726791 0.82170191 0.52046577]\n [0.84807446 0.70375552 0.31805087]\n [0.3812772  0.31083093 0.33218005]\n [0.49522332 0.4586895  0.61974004]\n [0.88130502 0.47469752 0.50149153]] \n Shape of data: (10, 3)\n \nX\n [[[0.58708034 0.88707951 0.25878656]]\n \n [[0.52696273 0.13857786 0.50993527]]\n \n [[0.53533872 0.45365456 0.89658186]]\n \n [[0.54978604 0.91198371 0.25040483]]\n \n [[0.36520302 0.76098129 0.5341683 ]]\n \n [[0.46726791 0.82170191 0.52046577]]\n \n [[0.84807446 0.70375552 0.31805087]]\n \n [[0.3812772  0.31083093 0.33218005]]\n \n [[0.49522332 0.4586895  0.61974004]]] \n Shape of X: (9, 1, 3)\n \nY\n [[[0.52696273 0.13857786 0.50993527]]\n \n [[0.53533872 0.45365456 0.89658186]]\n \n [[0.54978604 0.91198371 0.25040483]]\n \n [[0.36520302 0.76098129 0.5341683 ]]\n \n [[0.46726791 0.82170191 0.52046577]]\n \n [[0.84807446 0.70375552 0.31805087]]\n \n [[0.3812772  0.31083093 0.33218005]]\n \n [[0.49522332 0.4586895  0.61974004]]\n \n [[0.88130502 0.47469752 0.50149153]]] \n Shape of Y: (9, 1, 3)<\/pre>\n\n\n\n
Case 2: Forecasting times t+1, t+2, and t+3, utilizing sequential information from times t, t-1, and t-2<\/strong><\/p>\n\n\n\n
This involves a multistep forecasting approach utilizing sequential past information.<\/p>\n\n\n\n
# Generate suitable sequences for CNN, RNN, LSTM, and so on\nts_list = [-2,-1,0] # selected timesteps\nfh_list = [1,2,3]   # selected forecasting horizons\n \n# generate sequences dataset for Keras\nX, Y = f_make_seq_data_from_matrix(data, ts_list, fh_list)\n \nprint(\"\\nTimesteps:\", ts_list, \", forecast horizons:\", fh_list)\nprint(\"\\nData\\n\", data, \"\\n Shape of data:\", data.shape)\nprint(\"\\nX\\n\", X, \"\\n Shape of X:\", X.shape)\nprint(\"\\nY\\n\", Y, \"\\n Shape of Y:\", Y.shape)<\/pre>\n\n\n\n
Timesteps: [-2, -1, 0] , forecast horizons: [1, 2, 3]\n \nData\n [[0.58708034 0.88707951 0.25878656]\n [0.52696273 0.13857786 0.50993527]\n [0.53533872 0.45365456 0.89658186]\n [0.54978604 0.91198371 0.25040483]\n [0.36520302 0.76098129 0.5341683 ]\n [0.46726791 0.82170191 0.52046577]\n [0.84807446 0.70375552 0.31805087]\n [0.3812772  0.31083093 0.33218005]\n [0.49522332 0.4586895  0.61974004]\n [0.88130502 0.47469752 0.50149153]] \n Shape of data: (10, 3)\n \nX\n [[[0.58708034 0.88707951 0.25878656]\n  [0.52696273 0.13857786 0.50993527]\n  [0.53533872 0.45365456 0.89658186]]\n \n [[0.52696273 0.13857786 0.50993527]\n  [0.53533872 0.45365456 0.89658186]\n  [0.54978604 0.91198371 0.25040483]]\n \n [[0.53533872 0.45365456 0.89658186]\n  [0.54978604 0.91198371 0.25040483]\n  [0.36520302 0.76098129 0.5341683 ]]\n \n [[0.54978604 0.91198371 0.25040483]\n  [0.36520302 0.76098129 0.5341683 ]\n  [0.46726791 0.82170191 0.52046577]]\n \n [[0.36520302 0.76098129 0.5341683 ]\n  [0.46726791 0.82170191 0.52046577]\n  [0.84807446 0.70375552 0.31805087]]] \n Shape of X: (5, 3, 3)\n \nY\n [[[0.54978604 0.91198371 0.25040483]\n  [0.36520302 0.76098129 0.5341683 ]\n  [0.46726791 0.82170191 0.52046577]]\n \n [[0.36520302 0.76098129 0.5341683 ]\n  [0.46726791 0.82170191 0.52046577]\n  [0.84807446 0.70375552 0.31805087]]\n \n [[0.46726791 0.82170191 0.52046577]\n  [0.84807446 0.70375552 0.31805087]\n  [0.3812772  0.31083093 0.33218005]]\n \n [[0.84807446 0.70375552 0.31805087]\n  [0.3812772  0.31083093 0.33218005]\n  [0.49522332 0.4586895  0.61974004]]\n \n [[0.3812772  0.31083093 0.33218005]\n  [0.49522332 0.4586895  0.61974004]\n  [0.88130502 0.47469752 0.50149153]]] \n Shape of Y: (5, 3, 3)<\/pre>\n\n\n\n
Case 3: Forecasting at times t+3 and t+5 using nonconsecutive multistep forecasting with time t and t-2 as distributed lag information<\/strong><\/p>\n\n\n\n
This exercise isn’t realistic; however, it’s used to demonstrate the generalized characteristics of the function.<\/p>\n\n\n\n
# Generate suitable sequences for CNN, RNN, LSTM, and so on\nts_list = [-2,0] # selected timesteps\nfh_list = [3,5] # selected forecasting horizons\n \n# generate sequences dataset for Keras\nX, Y = f_make_seq_data_from_matrix(data, ts_list, fh_list)\n \nprint(\"\\nTimesteps:\", ts_list, \", forecast horizons:\", fh_list)\nprint(\"\\nData\\n\", data, \"\\n Shape of data:\", data.shape)\nprint(\"\\nX\\n\", X, \"\\n Shape of X:\", X.shape)\nprint(\"\\nY\\n\", Y, \"\\n Shape of Y:\", Y.shape)<\/pre>\n\n\n\n
Timesteps: [-2, 0] , forecast horizons: [3, 5]\n \nData\n [[0.58708034 0.88707951 0.25878656]\n [0.52696273 0.13857786 0.50993527]\n [0.53533872 0.45365456 0.89658186]\n [0.54978604 0.91198371 0.25040483]\n [0.36520302 0.76098129 0.5341683 ]\n [0.46726791 0.82170191 0.52046577]\n [0.84807446 0.70375552 0.31805087]\n [0.3812772  0.31083093 0.33218005]\n [0.49522332 0.4586895  0.61974004]\n [0.88130502 0.47469752 0.50149153]] \n Shape of data: (10, 3)\n \nX\n [[[0.58708034 0.88707951 0.25878656]\n  [0.53533872 0.45365456 0.89658186]]\n \n [[0.52696273 0.13857786 0.50993527]\n  [0.54978604 0.91198371 0.25040483]]\n \n [[0.53533872 0.45365456 0.89658186]\n  [0.36520302 0.76098129 0.5341683 ]]] \n Shape of X: (3, 2, 3)\n \nY\n [[[0.46726791 0.82170191 0.52046577]\n  [0.3812772  0.31083093 0.33218005]]\n \n [[0.84807446 0.70375552 0.31805087]\n  [0.49522332 0.4586895  0.61974004]]\n \n [[0.3812772  0.31083093 0.33218005]\n  [0.88130502 0.47469752 0.50149153]]] \n Shape of Y: (3, 2, 3)<\/pre>\n\n\n\n
Originally posted on SHLee AI Financial Model<\/a> blog.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"
This post constructs the multivariate time series data into sequence samples dataset for RNNs, LSTMs, CNNs, and similar models in Keras or 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