This post constructs the multivariate time series data into sequence samples dataset for RNNs, LSTMs, CNNs, and similar models in Keras or Tensorflow.
Time Series Sequence Samples Dataset
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.
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.
Python code
I’ve made a general function for this purpose:
f_make_seq_data_from_matrix(data, ts_list, fh_list) .
The ‘data‘ is a numpy matrix which contains a multivariate time series. ‘ts_list‘ is a list of timesteps, which doesn’t have to be consecutive. On the other hand, ‘fh_list‘ refers to a list of forecasting horizons, capable of representing single or multi-step forecasts and also need not be consecutive.
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.
import numpy as np def f_make_seq_data_from_matrix(data, ts_list, fh_list): co_list = ts_list+fh_list coseq_range = range(min(co_list),max(co_list)+1) tsseq_range = range(min(ts_list),max(ts_list)+1) fhseq_range = range(min(fh_list),max(fh_list)+1) tssel_list = [i - min(ts_list) for i in ts_list] fhsel_list = [i - min(fh_list) for i in fh_list] is_seq = []; ot_seq = []; obs = data.shape[0] for i in range(obs - len(coseq_range) + 1): dal = data[i:i + len(coseq_range)] din = dal[:len(tsseq_range)] dot = dal[-len(fhseq_range):] is_seq.append(din[tssel_list]) ot_seq.append(dot[fhsel_list]) return np.array(is_seq), np.array(ot_seq)
The elements of two lists are determined based on the time ‘t‘. For example, -2, -1, 0, 1, 2 correspond to t-2, t-1, t, t+1, t+2 respectively.
Case 1: Forecasting time t+1 utilizing information from time t
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.
# Suppose data has 10 observations with 3 features data = np.random.rand(10, 3) # Generate suitable sequences for CNN, RNN, LSTM, and so on ts_list = [0] # selected timesteps fh_list = [1] # selected forecasting horizons # generate sequences dataset for Keras X, Y = f_make_seq_data_from_matrix(data, ts_list, fh_list) print("\nTimesteps:", ts_list, ", forecast horizons:", fh_list) print("\nData\n", data, "\n Shape of data:", data.shape) print("\nX\n", X, "\n Shape of X:", X.shape) print("\nY\n", Y, "\n Shape of Y:", Y.shape)
Timesteps: [0] , forecast horizons: [1] Data [[0.58708034 0.88707951 0.25878656] [0.52696273 0.13857786 0.50993527] [0.53533872 0.45365456 0.89658186] [0.54978604 0.91198371 0.25040483] [0.36520302 0.76098129 0.5341683 ] [0.46726791 0.82170191 0.52046577] [0.84807446 0.70375552 0.31805087] [0.3812772 0.31083093 0.33218005] [0.49522332 0.4586895 0.61974004] [0.88130502 0.47469752 0.50149153]] Shape of data: (10, 3) X [[[0.58708034 0.88707951 0.25878656]] [[0.52696273 0.13857786 0.50993527]] [[0.53533872 0.45365456 0.89658186]] [[0.54978604 0.91198371 0.25040483]] [[0.36520302 0.76098129 0.5341683 ]] [[0.46726791 0.82170191 0.52046577]] [[0.84807446 0.70375552 0.31805087]] [[0.3812772 0.31083093 0.33218005]] [[0.49522332 0.4586895 0.61974004]]] Shape of X: (9, 1, 3) Y [[[0.52696273 0.13857786 0.50993527]] [[0.53533872 0.45365456 0.89658186]] [[0.54978604 0.91198371 0.25040483]] [[0.36520302 0.76098129 0.5341683 ]] [[0.46726791 0.82170191 0.52046577]] [[0.84807446 0.70375552 0.31805087]] [[0.3812772 0.31083093 0.33218005]] [[0.49522332 0.4586895 0.61974004]] [[0.88130502 0.47469752 0.50149153]]] Shape of Y: (9, 1, 3)
Case 2: Forecasting times t+1, t+2, and t+3, utilizing sequential information from times t, t-1, and t-2
This involves a multistep forecasting approach utilizing sequential past information.
# Generate suitable sequences for CNN, RNN, LSTM, and so on ts_list = [-2,-1,0] # selected timesteps fh_list = [1,2,3] # selected forecasting horizons # generate sequences dataset for Keras X, Y = f_make_seq_data_from_matrix(data, ts_list, fh_list) print("\nTimesteps:", ts_list, ", forecast horizons:", fh_list) print("\nData\n", data, "\n Shape of data:", data.shape) print("\nX\n", X, "\n Shape of X:", X.shape) print("\nY\n", Y, "\n Shape of Y:", Y.shape)
Timesteps: [-2, -1, 0] , forecast horizons: [1, 2, 3] Data [[0.58708034 0.88707951 0.25878656] [0.52696273 0.13857786 0.50993527] [0.53533872 0.45365456 0.89658186] [0.54978604 0.91198371 0.25040483] [0.36520302 0.76098129 0.5341683 ] [0.46726791 0.82170191 0.52046577] [0.84807446 0.70375552 0.31805087] [0.3812772 0.31083093 0.33218005] [0.49522332 0.4586895 0.61974004] [0.88130502 0.47469752 0.50149153]] Shape of data: (10, 3) X [[[0.58708034 0.88707951 0.25878656] [0.52696273 0.13857786 0.50993527] [0.53533872 0.45365456 0.89658186]] [[0.52696273 0.13857786 0.50993527] [0.53533872 0.45365456 0.89658186] [0.54978604 0.91198371 0.25040483]] [[0.53533872 0.45365456 0.89658186] [0.54978604 0.91198371 0.25040483] [0.36520302 0.76098129 0.5341683 ]] [[0.54978604 0.91198371 0.25040483] [0.36520302 0.76098129 0.5341683 ] [0.46726791 0.82170191 0.52046577]] [[0.36520302 0.76098129 0.5341683 ] [0.46726791 0.82170191 0.52046577] [0.84807446 0.70375552 0.31805087]]] Shape of X: (5, 3, 3) Y [[[0.54978604 0.91198371 0.25040483] [0.36520302 0.76098129 0.5341683 ] [0.46726791 0.82170191 0.52046577]] [[0.36520302 0.76098129 0.5341683 ] [0.46726791 0.82170191 0.52046577] [0.84807446 0.70375552 0.31805087]] [[0.46726791 0.82170191 0.52046577] [0.84807446 0.70375552 0.31805087] [0.3812772 0.31083093 0.33218005]] [[0.84807446 0.70375552 0.31805087] [0.3812772 0.31083093 0.33218005] [0.49522332 0.4586895 0.61974004]] [[0.3812772 0.31083093 0.33218005] [0.49522332 0.4586895 0.61974004] [0.88130502 0.47469752 0.50149153]]] Shape of Y: (5, 3, 3)
Case 3: Forecasting at times t+3 and t+5 using nonconsecutive multistep forecasting with time t and t-2 as distributed lag information
This exercise isn’t realistic; however, it’s used to demonstrate the generalized characteristics of the function.
# Generate suitable sequences for CNN, RNN, LSTM, and so on ts_list = [-2,0] # selected timesteps fh_list = [3,5] # selected forecasting horizons # generate sequences dataset for Keras X, Y = f_make_seq_data_from_matrix(data, ts_list, fh_list) print("\nTimesteps:", ts_list, ", forecast horizons:", fh_list) print("\nData\n", data, "\n Shape of data:", data.shape) print("\nX\n", X, "\n Shape of X:", X.shape) print("\nY\n", Y, "\n Shape of Y:", Y.shape)
Timesteps: [-2, 0] , forecast horizons: [3, 5] Data [[0.58708034 0.88707951 0.25878656] [0.52696273 0.13857786 0.50993527] [0.53533872 0.45365456 0.89658186] [0.54978604 0.91198371 0.25040483] [0.36520302 0.76098129 0.5341683 ] [0.46726791 0.82170191 0.52046577] [0.84807446 0.70375552 0.31805087] [0.3812772 0.31083093 0.33218005] [0.49522332 0.4586895 0.61974004] [0.88130502 0.47469752 0.50149153]] Shape of data: (10, 3) X [[[0.58708034 0.88707951 0.25878656] [0.53533872 0.45365456 0.89658186]] [[0.52696273 0.13857786 0.50993527] [0.54978604 0.91198371 0.25040483]] [[0.53533872 0.45365456 0.89658186] [0.36520302 0.76098129 0.5341683 ]]] Shape of X: (3, 2, 3) Y [[[0.46726791 0.82170191 0.52046577] [0.3812772 0.31083093 0.33218005]] [[0.84807446 0.70375552 0.31805087] [0.49522332 0.4586895 0.61974004]] [[0.3812772 0.31083093 0.33218005] [0.88130502 0.47469752 0.50149153]]] Shape of Y: (3, 2, 3)
Originally posted on SHLee AI Financial Model blog.
Disclosure: Interactive Brokers
Information posted on IBKR Campus that is provided by third-parties does NOT constitute a recommendation that you should contract for the services of that third party. Third-party participants who contribute to IBKR Campus are independent of Interactive Brokers and Interactive Brokers does not make any representations or warranties concerning the services offered, their past or future performance, or the accuracy of the information provided by the third party. Past performance is no guarantee of future results.
This material is from SHLee AI Financial Model and is being posted with its permission. The views expressed in this material are solely those of the author and/or SHLee AI Financial Model and Interactive Brokers is not endorsing or recommending any investment or trading discussed in the material. This material is not and should not be construed as an offer to buy or sell any security. It should not be construed as research or investment advice or a recommendation to buy, sell or hold any security or commodity. This material does not and is not intended to take into account the particular financial conditions, investment objectives or requirements of individual customers. Before acting on this material, you should consider whether it is suitable for your particular circumstances and, as necessary, seek professional advice.
Join The Conversation
If you have a general question, it may already be covered in our FAQs. If you have an account-specific question or concern, please reach out to Client Services.