# Virtually increase the size of sample data

I have a general problem linked to forecasts. I have an operational task to perform and I chose to fit simple models to the data.

I would like to have a 6-month forecast month by month for potential orders. The problem is that I have data from 2011, which consists of less than 60 weekly samples. The output forecast is generally flat for each item.

Is it possible to virtually increase the sample data by computing orders week by week, then forecasting 6*4 = 24 weeks and finally aggregate forecast for each month?

• It is unclear what is your data and what you want to do... It is not even clear if your data is weekly or monthly based? What you want to forecast? Why you want to do it? Why you want to aggregate something? – Tim Jan 15 '16 at 13:48
• @Tim More details is better, but I think he stated the main issue in sufficient detail, his problem is quite common in forecasting – Aksakal Jan 15 '16 at 14:13

You're talking about increasing the sampling frequency from monthly to weekly AND decreasing the forecasting step. Now your forecast is weekly, but you aggregate it afterwards to monthly. So the native frequency is still weekly.

Hence, it's not just 'virtually' increasing the sample size alone. To increase the sample size without changing the forecasting step you could use overlapping periods, i.e. your forecast step is still monthly but sampling frequency is weekly now. That will bulk up your sample size. Obviously, this comes at a price: your data is even more autocorrelated now. The overlapping monthly periods will make it highly autocorrelated.

There are ways to deal with autocorrelation though, e.g. look at this paper on example of using Newey-West estimator and other ways of dealing with overlapping data.

There are advantages of using overlapping periods, so don't be scared with complications. It's a trade-off, and you have to weigh in the pluses and minuses to decide whether it's appropriate for your case.

Now, the main question: will any of this improve your forecast? It seems that your complaint is that your forecast lacks features, i.e. flat as you put it. You're probably using a time series model, such as AR(p). These tend to produce flat forecasts in long run as their solutions are stationary. You see the typical forecasts on the pic below, they all sort of revert to a mean. For instance, $x_t = c+\beta x_{t-1}+e_t$ will revert to $\frac{c}{1-\beta}$ in long run.

On the other hand in the near term increasing the sampling frequency and decreasing forecasting step will lead to capturing higher frequencies in short term. In other words your forecast will be less flat, have more features in first few weeks of forecast. However, in the long run these ripples will disappear, since the sample range hasn't changed: it's still from 2011, hence, the long waves are the same.

Intuitively how far you can see depends on how far back your data goes. Farther backwards your data goes, farther forward you'll see the details. Increasing frequency of your sample doesn't help you see farther forward, but it helps to see more details in near future.