ConvLSTM<\/li>\n<\/ol>\nEach of these models are demonstrated for one-step univariate time series forecasting, but can easily be adapted and used as the input part of a model for other types of time series forecasting problems.<\/p>\n
Data Preparation<\/h3>\n
Before a univariate series can be modeled, it must be prepared.<\/p>\n
The LSTM model will learn a function that maps a sequence of past observations as input to an output observation. As such, the sequence of observations must be transformed into multiple examples from which the LSTM can learn.<\/p>\n
Consider a given univariate sequence:<\/p>\n
[10, 20, 30, 40, 50, 60, 70, 80, 90]<\/pre>\nWe can divide the sequence into multiple input\/output patterns called samples, where three time steps are used as input and one time step is used as output for the one-step prediction that is being learned.<\/p>\n
X,\t\t\t\ty\r\n10, 20, 30\t\t40\r\n20, 30, 40\t\t50\r\n30, 40, 50\t\t60\r\n...<\/pre>\nThe split_sequence()<\/em> function below implements this behavior and will split a given univariate sequence into multiple samples where each sample has a specified number of time steps and the output is a single time step.<\/p>\n# split a univariate sequence into samples\r\ndef split_sequence(sequence, n_steps):\r\n\tX, y = list(), list()\r\n\tfor i in range(len(sequence)):\r\n\t\t# find the end of this pattern\r\n\t\tend_ix = i + n_steps\r\n\t\t# check if we are beyond the sequence\r\n\t\tif end_ix > len(sequence)-1:\r\n\t\t\tbreak\r\n\t\t# gather input and output parts of the pattern\r\n\t\tseq_x, seq_y = sequence[i:end_ix], sequence[end_ix]\r\n\t\tX.append(seq_x)\r\n\t\ty.append(seq_y)\r\n\treturn array(X), array(y)<\/pre>\nWe can demonstrate this function on our small contrived dataset above.<\/p>\n
The complete example is listed below.<\/p>\n
# univariate data preparation\r\nfrom numpy import array\r\n\r\n# split a univariate sequence into samples\r\ndef split_sequence(sequence, n_steps):\r\n\tX, y = list(), list()\r\n\tfor i in range(len(sequence)):\r\n\t\t# find the end of this pattern\r\n\t\tend_ix = i + n_steps\r\n\t\t# check if we are beyond the sequence\r\n\t\tif end_ix > len(sequence)-1:\r\n\t\t\tbreak\r\n\t\t# gather input and output parts of the pattern\r\n\t\tseq_x, seq_y = sequence[i:end_ix], sequence[end_ix]\r\n\t\tX.append(seq_x)\r\n\t\ty.append(seq_y)\r\n\treturn array(X), array(y)\r\n\r\n# define input sequence\r\nraw_seq = [10, 20, 30, 40, 50, 60, 70, 80, 90]\r\n# choose a number of time steps\r\nn_steps = 3\r\n# split into samples\r\nX, y = split_sequence(raw_seq, n_steps)\r\n# summarize the data\r\nfor i in range(len(X)):\r\n\tprint(X[i], y[i])<\/pre>\nRunning the example splits the univariate series into six samples where each sample has three input time steps and one output time step.<\/p>\n
[10 20 30] 40\r\n[20 30 40] 50\r\n[30 40 50] 60\r\n[40 50 60] 70\r\n[50 60 70] 80\r\n[60 70 80] 90<\/pre>\nNow that we know how to prepare a univariate series for modeling, let\u2019s look at developing LSTM models that can learn the mapping of inputs to outputs, starting with a Vanilla LSTM.<\/p>\n<\/p>\n
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