# Delay issue in time series prediction

I am having an issue using neural networks to predict time series. Some predicted data fits with the expected data, as bellow: (In black the real time series and in blue the output of my neural network)

Time serie: Australia energy demand.

But with the same code, with other time series, the predicted data does not fits with the expected data, and has a delay of one unit, as bellow:

Time serie: Walmart Stock price. Time serie: Dollar libra exchange.

I found some articles about some variations of neural networks and at the results section shows the plot with the delay like my results, as bellow:

Time serie: Dollar libra exchange. (Article link: http://www.sciencedirect.com/science/article/pii/S1877050915015793)

Anyone knows if this is a common behavior or can be something wrong with my code ? I am having this issue about three months ago, and since there I am trying to figure out some bug in my code but is all right.

Thanks and I appreciate any tip.

• What type of neural network are you using and what are your parameters? – noumenal Feb 19 '16 at 20:23
• @noumenal I am using the Extreme Learning Machine. Source code ntu.edu.sg/home/egbhuang/elm_codes.html. Each data set has different parameters. – ViniciusArruda Feb 22 '16 at 13:26

A random walk (without drift) would be specified as follows; $$y_t = y_{t-1} + \varepsilon_t$$ where $E[e_t] = 0$. Thus $E[Y_t|y_1,...,y_{t-1}] = y_{t-1}$. So when you graph your predictions against actual observations, it will look as though your predictions are delayed by one unit, when in fact the forecasts are just using the contemporaneous observation as next periods prediction.