univariate time series multi step ahead prediction using multi-layer-perceptron(MLP)

Question

I have a univariate time series data. I want to do a multistep prediction.

I came across this question which explains time series one step prediction. but I am interested in multistep ahead prediction.

e.g typical univariate time series data looks like

    time  value
    ----  ------
    t1      a1
    t2      a2
    ..........
    ..........
    t100    a100.

Suppose, I want 3 step ahead prediction. Can I frame my problem like

   TrainX                 TrainY
[a1,a2,a3,a4,a5,a6]   -> [a7,a8,a9]
[a2,a3,a4,a5,a6,a7]   -> [a8,a9,a10]
[a3,a4,a5,a6,a7,a8]   -> [a9,a10,a11]
..................        ...........
..................        ...........

I am using keras and tensorflow as backend

First layer has 50 neurons and expects 6 inputs. hidden layer has 30 neurons output layer has 3 neurons i.e (outputs three time series values)

model = Sequential()
model.add(Dense(50, input_dim=6, activation='relu',kernel_regularizer=regularizers.l2(0.01)))
model.add(Dense(30, activation='relu',kernel_regularizer=regularizers.l2(0.01)))
model.add(Dense(3))
model.compile(loss='mean_squared_error', optimizer='adam')

model.fit(TrainX, TrainY, epochs=300, batch_size=16)

My model will be able to predict a107,a108,a109 ,when my input is a101,a102,a103,a104,a105,a106 Is this a valid model ? Am I missing some thing?

Answer 1

That model might do it, but you should probably benefit from using LSTM layers (recurrent networks for sequences).

#TrainX.shape = (total of samples, time steps, features per step)   
#TrainX.shape = (total of samples, 6, 1)

model.add(LSTM(50,input_shape=(6,1),return_sequences=True, ....))
model.add(LSTM(30,return_sequences=True, ....))
model.add(LSTM(3,return_sequences=False, ....))

You may be missing an activation function that limits the result to the possible range of the value you want to predict.

Often we work with values from 0 to 1 (activation='sigmoid') or from -1 to 1 (activation='tanh').
This would also require that the input be limited to these values, since inputs and outputs are the same.