Building a time-series demand forecasting model

Question

I am forecasting demand for certain types of goods and services, which I expect to be correlated to a sub-set of a basket of macroeconomic indicators (considering 15-20 indicators)

I do not know which indicators influence the demand more, whether they have a simple correlation influence or whether a derivative of change influences the demand (i.e. GDP or GDP change for example) or whether there’s a delayed effect on demand (e.g. increased government spend in last year may better predict this year’s demand?). Some macro indicators may be correlated to each other.

I have some basic hypotheses on likely indicators - that may be right or wrong.

Questions 1. What are good time-series forecasting models? What can be considered, apart from just a multivariate regression? 2. Is there a tool whereby I can input the historical demand, historical macro indicators, which will then output which set of indicators best predict the demand and which model works best?

I know how to do regressions in excel, but that’s just one set of indicators at a time. 20 indicators (plus derivatives, plus lag) throws up so many possibilities I cannot manually simulate.

Any help appreciated.

Answer 1

1. If it's just knowing about the models, I'd suggest starting with Hamilton's "Time Series Analysis" but any book like it will do. You can also explore Google Scholar for inspiration (people likely had built similar models). It seems you have a VAR model, check this wikipedia link to see if it's what you have in mind: https://en.wikipedia.org/wiki/Vector_autoregression

2. If you are looking for tools to obtain these forecasts, I'd suggest EViews or R. They are not useful on their own: you must have to have a model to do any kind of forecasting.

Answer 2

It doesn't seem like your problem is related to the time series nature of the problem. It seems like your problem is that you have "too many" possible independent variables, and the "kitchen sink" approach of regressing on all of them is creating multi-colinearity or very low predictive ability, say as measured by $r^2$.

What you should do instead is use a model selection method like the LASSO to pick variables in order to minimize your prediction error. You give the LASSO all the variables and combinations of variables you think are at all relevant, and LASSO will decide how many and which to include in your predictive model. The key to this is that it splits your data into different "folds", and cross-tests the proposed models on all these different "data sets". This ensures that your model will do a good job predicting out-of-sample.

One trade-off is that you cannot do this in excel, unless excel has really changed since the last time I used it. You need a real statistics package, like eviews, STATA, or R. R is free, however, and many people are doing things like what you suggest; the package you want is called glmnet. The other trade-off is that machine learning methods like the LASSO introduce bias in the estimates of the coefficients in order to minimize expected prediction error, so that your model is intended to PREDICT what is going to happen, but not EXPLAIN why: do not look at the coefficients on the variables and try to interpret them as causal marginal effects.