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I'm working with timeseries forecasting with daily granularity data and I have a hypothetical question. What is the optimal forecast window for timeseries forecasting ? Say we have 1 year historical data, what should be the optimal forecast window. Is there any literature or rule of thumb for the same ?

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    $\begingroup$ By "window", do you mean how much past data to use? Or how far to forecast out into the future? $\endgroup$ – S. Kolassa - Reinstate Monica Sep 30 '15 at 11:27
  • $\begingroup$ @StephanKolassa: How far to forecast into the future $\endgroup$ – psteelk Sep 30 '15 at 17:04
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Using "window" to mean "how far to forecast into the future" is nonstandard usage. "Window" more frequently refers to a subsample of the past series, as in taking rolling means over a three-period window. You can see from the answers that this usage is confusing to experts. I recommend that you use the more common term "forecast horizon".


As to your question: there is no "optimal" forecast horizon. You use the horizon you need for subsequent processes that use your forecast. For instance, I do forecasting for supermarkets.

  • Sometimes I am interested in forecasts for the next five days (when generating replenishment orders from distribution centers, since each order typically only needs to cover three to five days' demand).

  • Sometimes I am interested in two weeks (when doing some more fancy optimization on replenishment).

  • Sometimes I am interested in three months (when planning promotional activities, price reductions and marketing, to notify suppliers).

  • As @Aksakal notes, sometimes you have to satisfy regulations that prescribe a certain forecasting horizon.

  • Demographical forecasting will typically use forecasting horizons on the order of decades.

  • And climate forecasting can look ahead for centuries.

In each case, you need forecasts for a certain horizon to support your decision-making today. (A two-year-ahead climate forecast won't help you in setting policy today.) And forecasting farther out than you need is useless. (No supermarket manager will be interested in a two-year-ahead forecast. The retailer's central strategy and planning department may well be.)

So: decide based on what you will use the forecast for.

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I don't think there is optimal forecast horizon. You can talk about maximum horizon, of course, which depends on the domain and the underlying process. Then again, there's no general rule of thumb.

For instance, in some applications in finance such as market value-at-risk of a portfolio, it's prescribed by regulators to produce 1 or 10 day ahead 99% confidence VaR number based on 12 months of data. VaR is essentially a tail of the distribution of profits and losses (or returns). In this regard VaR is a forecast of sorts.

In many economic applications, we have annual, quarterly, monthly and weekly seasonality. Obviously, you can't estimate annual and quarterly seasonality adjustments with one year data. Also, we prefer to have data over at least one business cycle, i.e. include boom/bust periods, which implies many years of data. Hence, in these applications with one year history your forecast horizon is limited with a couple of months, beyond which the forecast is questionable.

A good analogy is extrapolation. Extrapolation becomes unreliable when you step farther outside the data points.

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One year of daily data would be insufficient to estimate/identify annual repetitive activity. It would be sufficient to characterize day-of-the-week structure but even then holiday effects would distort them. As @stephan-kolassa pointed out the preferred term is forecast horizon not "window" but I for one did understand what you meant by window. In terms of optimal "window ahead" (forecast horizon) there is no "optimal" but there can be ever-increasing uncertainty which might be a mitigating factor when selecting an appropriate "window" or "horizon". Normally this is set by the objective/need of the forecasting activity. Certainly without incorporating weekly/monthly/holiday effects any forecast might be in jeopardy.

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  • $\begingroup$ Given the OP's clarification that "window" means "how far to forecast into the future" (better known as "forecast horizon"), this does not answer the question. I'd recommend that you delete it. $\endgroup$ – S. Kolassa - Reinstate Monica Oct 1 '15 at 6:16
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As @IrishStat has nicely put, a daily data of one year would be sufficient if it accomodates the trends, activity and seasonality. However, some trends(and/or) seasonality might not be captured even by the daily frequency. They might require data captured every minute for explaining the effects.

So, a rule of thumb would be, if the frequency of data captured has the trends and seasonality which can explain your problem statement(or objective), then that would be the ideal window.


A quick search returned this piece of literature about Window Selection for Out-of-Sample Forecasting with Time-Varying Parameters by Atsushi et al. ; they talk about a novel method for selecting the estimation window size for forecasting.

Thought it might be of interest to you, so I attached it.

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  • $\begingroup$ Given the OP's clarification that "window" means "how far to forecast into the future" (better known as "forecast horizon"), this does not answer the question. I'd recommend that you delete it. $\endgroup$ – S. Kolassa - Reinstate Monica Oct 1 '15 at 6:15

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