Solved – How to Use Neural Networks to Forecast Time Series Data with Predictor Variables

forecastingmachine learningneural networkspredictorregression

I have browsed a lot of topics here, but the ones I see were all about forecasting a single variable, depending on its historical values. Whereas I want to predict a variable, by estimating a relationship between multiple predictor variables as well.

So I'm trying to find a function $f(x_1,x_2, … , x_p) = y$

-How- Can I apply a neural network approach for such a task?

If not, what alternatives can I use for this?

Edit :

I am trying to implement this in MATLAB, so I would really appreciate some MATLAB implementation of such methods.

Best Answer

you should consider a matrix of samples $X\in \mathbb R^{n\times p}$ where each column is a different variable and each rows is a different samples that is a discrete representation of your time series. After that you can train a neural network with input $X$ and output $y$ as if it is a simple polynomial interpolation.

The problem is actually more complex but this could probably be a starting point

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Solved – Time series analysis with neural networks

A feed-forward neural network (typically multi-layer) is a type of supervised learner that will adjust the network weights on its input and internal nodes, in an iterative manner, in order to minimize errors between predicted and actual target variables. It commonly uses stochastic gradient descent (sometimes called error back propagation) over many iterations in order to find a local minimum of the error response and optimize the network weights accordingly.

The basic idea behind stochastic gradient descent is to start by randomizing the weights, then adjust them by iterating through several passes and updating the weights in a direction that moves the total error between target and predicted errors towards the local minimum error of the gradient surface. In practice, a tradeoff is found between optimizing a training set against a validation set, in order to reduce the problem of over-fitting.

Lastly, the input (time series or otherwise) often needs to be transformed in order to create a stationary series that is also bounded (amplitude wise) between the input range of the NN layer transfer function(s)(typically, 0 to 1 or -1 to 1).

Once the weights have been trained, the model can be stored and used to process additional new time series data, much like a typical linear regression based model.

An example illustration of using a NN to predict finanacial time series data, using Weka, is posted here: http://intelligenttradingtech.blogspot.com/2010/01/systems.html

A good text comparing financial AR based models against NN models is, "Applied Quantitative Methods for Trading and Investment," Christian Dunis et.al.

Forecasting Hourly Time Series with Daily, Weekly & Annual Periodicities

Unfortunately your mission is doomed to failure since you are restricted to R and SPSS. You need to identify lead and lag relationship structure for each of the events/holidays/exogenous variables that may come into play. You need to detect possible Time Trends which SPSS can't do. You need to incorporate Daily Trends / Predictions into each of the hourly forecasts in order to provide a consolidated.reeconciled forecast. You need to be concerned with changing parameters and changing variance. Hope this helps. We have been modelling this kind of data for years in an automatic manner, subject of course to optional user-specified controls.

EDIT: As OP requested I present here a typical analysis. I took one if the busier hours and developed a daily model. In a complete analysis all 24 hours would be developed and also a daily model in order to reconcile the forecasts. Following is a partial list of the model enter image description here . In addition to the significant regressors (note the actual lead and lag structure have been omitted ) there were indicators reflecting the seasonality , level shifts , daily effects , changes in daily effects , and unusual values not consistent with history. The model statistics are enter image description here . A plot of the forecasts for the next 360 days is shown here . The Actual/Fit/Forecast graph neatly summarizes the results .When faced with a tremendously complex problem (like this one!) one needs to show up with a lot of courage , experience and computer productivity aids. Just advise your management that the problem is solvable but not necessarily by using primitive tools. I hope this gives you encouragement to continue in your efforts as your previous comments have been very professional, geared towards personal enrichment and learning. I would add that one needs to know the expected value of this analysis and use that as a guideline when considering additional software. Perhaps you need a louder voice to help direct your "directors" towards a feasible solution to this challenging task.

After reviewing the Daily Totals and each of the 24 Hourly Models , I would definitely reflect that the Number Of Visits is in a serious downslide ! This kind of analysis by a prospective buyer would suggest a non-purchase while a seller would be wise to redouble their efforts to sell the business based upon this very negative projection.

Edit :

Best Answer

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Solved – Time series analysis with neural networks

Forecasting Hourly Time Series with Daily, Weekly & Annual Periodicities

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