People get married in summer and prefer to die in winter

The presence of seasonal patterns in many time series is not a big discovery. However, from time to time, interesting seasonal data come to you to teach you something it was no so obvious, at least for you. This happened to me recently when I was working with data of weddings and deaths in Spain for the last years in order to fit some basic ARIMA models to the data. I had an explanation for why do people decide to get married in summer because of the weather but the decision to die is not so clear, at least under normal circumstances.

Weddings and deaths in Spain from 2007 to 2013. Source:

Before seeing this plot, I would have betted a couple of beers that there was no relationship between the month and the number of deaths. Surprisingly, the reverse is true. It seems that the weather not only has an effect on weddings (nobody likes rain in his/her wedding day) but also on deaths, and the reasons are far from clear. One can think of a number of causes for this behavior but this is another question. In this post, my purpose is to show the importance of seasonality in predicting. In the context of general regression models, years, months, weeks and days are usually more important than we expected. Most of the times, plots rather than data tables allow practitioners to a better understanding of what is going on. In the search for features that are able to explain the behavior of any target variable, we are prone to look for a number of more difficult to obtain features, in terms of time and money. However, when dealing with time series forecasting, there are several features such as calendar variables that are cost free but that may be able to explain a remarkable part of the variance of the target variable. Two examples are weddings and deaths grouped by month but there are many other examples were seasonality is also present. Electricity consumption by hour, the effect of the day of the week and the January effect in stock market returns are examples on how seasonality and other calendar anomalies can lead users to important savings and benefits if they take into account these effects in their predictions. In the corporate cash management problem, one of the most important tasks is daily cash forecasting where the day-of-month and the day-of-week plays a critical role in the ability to predict next day cash flow. Setting one or two fixed days of payment per month is a common business practice so that cash flow highly depends on the day of the month that occurs. In this sense, the works on daily cash flow forecasting by Stone, Stone and Wood, and Miller and Stone in the seventies and eighties focus on the ability of calendar dummy variables for predictions. My first steps in daily cash flow forecasting confirm that the use of these calendar dummy variables results in better forecast accuracy. Remember, seasonality is present in weddings and deaths but also in cash flow forecasting and many other fields of interest for researchers. You can find useful information about seasonality in daily cash flow forecasting in the next references.

  • Stone, B. K. (1976). The payments-pattern approach to the forecasting and control of accounts receivable. Financial Management, 65-82.
  •  Stone, B. K., & Wood, R. A. (1977). Daily cash forecasting: a simple method for implementing the distribution approach. Financial Management, 40-50.
  •  Miller, T. W., & Stone, B. K. (1985). Daily Cash Forecasting and Seasonal Resolution: Alternative Models and Techniques for Using the Distribution Approach. Journal of Financial and Quantitative Analysis20(03), 335-351.
  •  Stone, B. K., & Miller, T. W. (1987). Daily cash forecasting with multiplicative models of cash flow patterns. Financial Management, 45-54.

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