Best forecasting model for time series analysis on small dataset

Question

I'm building a model which predicts the GDP(Quarterly) of my country. I've lots of time-series predictors(~50(Monthly), all continuous, e.g. Index of Industrial Production, etc.) but my dataset size is small(~120). I've tried using ARIMA(5,1,0) on GDP values:

I'm looking for a model which could take into account how predictors affect GDP along with past GDP values.

Should I try using Recurrent Neural Nets on such small dataset?

Also, I used log-transform to account of increasing variance in GDP values, which still hasn't solved the issue completely. Any suggestions on how to solve this would be amazing.

I'm using Python.

What do you mean by "predicts"? You need the future values of your predictors for that. Where do you get them? — Aksakal, Nov 15 '17 at 15:02
@Aksakal Edited my questions. Thanks for pointing out. I'm obtaining my predictors at monthly interval, so perhaps if a model can take into account GDP for January and predictor values for January, Feb. and March to predict the GDP for April. — Aman Gill, Nov 15 '17 at 15:26
Do you mean to say that you want to forecast GDP between its quarterly releases based on the already available monthly predictors? That's called "nowcasting", google it. It's very popular in US to nowcast GDP and other slow frequency series. — Aksakal, Nov 15 '17 at 15:39
See the works of Ines Wilms on sparse estimation of VAR models [here](https://feb.kuleuven.be/Ines.Wilms/papers%20). This is directly relevant for forecasting a high number of interrelated short time series. See especially Wilms I., Basu S., Bien J. and Matteson D.S. (2017), ["Sparse identification and estimation of vector autoregressive moving averages"](https://arxiv.org/abs/1707.09208). — Richard Hardy, Nov 15 '17 at 16:58
Why do you want a nonlinear model? You have little data, which justifies the choice of a simple (linear) model, yet you want a complicated (nonlinear) one. Also, you might want to think what kind of nonlinear model could make sense for your data before trying a random kind. — Richard Hardy, Nov 16 '17 at 12:47

score 2 · Accepted Answer · answered Nov 15 '17 at 15:36

2

Your focal time series and the "predictors" are interrelated. You might as well want to forecast the Index of Industrial Production, using GDP as a "predictor".

The classical approach to such a problem is Vector Autoregression (VAR), which models - and forecasts - the relationships between your series, as well as the time dynamics.

Such problems are the bread and butter of econometricians. I suggest you pick up pretty much any econometric textbook, perhaps looking for one that uses software you are comfortable with, such as Python.

answered Nov 15 '17 at 15:36

Stephan Kolassa

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Shouldn't I consider all my predictors as exogeneous variables and just my GDP depending on them. Being new to Time-Series analysis, I can't understand why forecasting IIP using GDP should improve my GDP forecast. – Aman Gill Nov 15 '17 at 16:24
I'm not saying that would improve the GDP forecast. I am saying that you could reasonably exchange the roles of "dependent time series" and "predictor": the problem is symmetric. In contrast, it wouldn't make sense to exchange the roles if retail sales were the dependent series and promotions the predictor, or if credit default were the dependent variable and income the predictor. – Stephan Kolassa Nov 15 '17 at 16:29
I see your point. Will try out VAR. Thanks for the answer. – Aman Gill Nov 15 '17 at 16:33
@AmanGill, See the works of Ines Wilms on sparse estimation of VAR models [here](https://feb.kuleuven.be/Ines.Wilms/papers%20). This is directly relevant for forecasting a high number of interrelated short time series. See especially Wilms I., Basu S., Bien J. and Matteson D.S. (2017), ["Sparse identification and estimation of vector autoregressive moving averages"](https://arxiv.org/abs/1707.09208). – Richard Hardy Nov 15 '17 at 16:58
@RichardHardy Are Dynamic Factor models same as VAR? – Aman Gill Nov 16 '17 at 08:11
@AmanGill, no, but some people estimate factors as a first step and then use them in a VAR in the second step. – Richard Hardy Nov 16 '17 at 09:03
@RichardHardy Can you suggest some Non-Linear statistic models for my problem. – Aman Gill Nov 16 '17 at 12:14

Aksakal · Answer 2 · 2017-11-15T17:01:50.837

There is a lot of literature on nowcasting in general, and GDP in particular. For instance, check GDPNow page on FRB Atlanta's web site, where the model description is given too. Below is their 2017 Q4 GPD forecast. As you know the GDP number release will be some time in 2018, i.e. a few months down the road from the time I'm posting my ansqwer.

Nowcasting is used to estimate the low frequency data based on high frequency predictors. For instance, CPI and Unemployment are released monthly, the interest rates are available either real time or at least daily. You could use these as predictors to estimate GDP between its quarterly releases.

Nowcasting is different from ordinary time series forecasting in that it has no issue with predicting the predictors. For instance, if you were to predict GDP one year ahead, you'd need values of its predictors one year ahead.

score 0 · Answer 3 · answered Nov 15 '17 at 15:07

it appears to me that the error variance changed deterministically at two points in time . See http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html . I was responsible for seamlessly integrating this along with Intervention Detection into a commercial package that I helped to develop. The implementation was for both ARIMA and Transfer Function (causal) Models.

Whereas the Box-Cox test When (and why) should you take the log of a distribution (of numbers)? remedies a linkage between the expected value and the variance, the TSAY test leads to GLS .

Best forecasting model for time series analysis on small dataset

3 Answers3