Time-series methods of forecasting

         Forecasting is a method or a technique for estimating future aspects of a business or the operation. It is a method for translating past data or experience into estimates of the future. It is a tool, which helps management in its attempts to cope with the uncertainty of the future. Forecasts are important for short-term and long-term decisions. Businesses may use forecast in several areas: technological forecast, economic forecast, demand forecast. There two broad categories of forecasting techniques: quantitative methods (objective approach) and qualitative methods (subjective approach). Quantitative forecasting methods are based on analysis of historical data and assume that past patterns in data can be used to forecast future data points. Qualitative forecasting techniques employ the judgment of experts in specified field to generate forecasts. They are based on educated guesses or opinions of experts in that area. There are two types of quantitative methods: Times-series method and explanatory methods.

         Time-series methods make forecasts based solely on historical patterns in the data. Time-series methods use time as independent variable to produce demand. In a time series, measurements are taken at successive points or over successive periods. The measurements may be taken every hour, day, week, month, or year, or at any other regular (or irregular) interval. A first step in using time-series approach is to gather historical data. The historical data is representative of the conditions expected in the future. Time-series models are adequate forecasting tools if demand has shown a consistent pattern in the past that is expected to recur in the future. For example, new homebuilders in US may see variation in sales from month to month. But analysis of past years of data may reveal that sales of new homes are increased gradually over period of time. In this case trend is increase in new home sales. Time series models are characterized of four components: trend component, cyclical component, seasonal component, and irregular component. Trend is important characteristics of time series models. Although times series may display trend, there might be data points lying above or below trend line. Any recurring sequence of points above and below the trend line that last for more than a year is considered to constitute the cyclical component of the time series—that is, these observations in the time series deviate from the trend due to fluctuations. The real Gross Domestics Product (GDP) provides good examples of a time series tat displays cyclical behavior. The component of the time series that captures the variability in the data due to seasonal fluctuations is called the seasonal component. The seasonal component is similar to the cyclical component in that they both refer to some regular fluctuations in a time series. Seasonal components capture the regular pattern of variability in the time series within one-year periods. Seasonal commodities are best examples for seasonal components. Random variations in times series is represented by the irregular component. The irregular component of the time series cannot be predicted in advance. The random variations in the time series are caused by short-term, unanticipated and nonrecurring factors that affect the time series.

            Smoothing methods (stable series) are appropriate when a time series displays no significant effects of trend, cyclical, or seasonal components. In such a case, the goal is to smooth out the irregular component of the time series by using an averaging process. The moving averages method is the most widely used smoothing technique. In this method, the forecast is the average of the last “x” number of observations, where “x” is some suitable number. Suppose a forecaster wants to generate three-period moving averages. In the three-period example, the moving averages method would use the average of the most recent three observations of data in the time series as the forecast for the next period. This forecasted value for the next period, in conjunction with the last two observations of the historical time series, would yield an average that can be used as the forecast for the second period in the future. The calculation of a three-period moving average is illustrated in following table. Based on the three-period moving averages, the forecast may predict that 2.55 million new homes are most likely to be sold in the US in year 2008.

Year	Actual sale(in million)	Forecast(in million)	Calculation
2003	4
2004	3
2005	2
2006	1.5	3	(4+3+2)/3
2007	1	2.67	(3+2+3)/3
2008		2.55	(2+3+2.67)/3

Example: Three-period moving averages

In calculating moving averages to generate forecasts, the forecaster may experiment with different-length moving averages. The forecaster will choose the length that yields the highest accuracy for the forecasts generated. Weighted moving averages method is a variant of moving average approach. In the moving averages method, each observation of data receives the same weight. In the weighted moving averages method, different weights are assigned to the observations on data that are used in calculating the moving averages. Suppose, once again, that a forecaster wants to generate three-period moving averages. Under the weighted moving averages method, the three data points would receive different weights before the average is calculated. Generally, the most recent observation receives the maximum weight, with the weight assigned decreasing for older data values.

Year	Actual sale(in million)	Forecast(in million)	Calculation
2005	2 (.2)
2006	1.5 (.3)
2007	1 (.4)
2008		.42	(2*.2+1.5*.3+1*.4)/3

Example: Weighted three-period moving averages method

A more complex form of weighted moving average is exponential smoothing. I this method the weight fall off exponentially as the data ages. Exponential smoothing takes the previous period’s forecast and adjusts it by a predetermined smoothing constant, ά (called alpha; the value for alpha is less than one) multiplied by the difference in the previous forecast and the demand that actually occurred during the previously forecasted period (called forecast error). Exponential smoothing is mathematically represented as follows: New forecast = previous forecast + alpha (actual demand − previous forecast) Or can be formulated as  F = F + ά(D − F)

         Other time-series forecasting methods are, forecasting using trend projection, forecasting using trend and seasonal components and causal method of forecasting. Trend projection method used the underlying long-term trend of time series of data to forecast its future values. Trend and seasonal components method uses seasonal component of a time series in addition to the trend component. Causal methods use the cause-and-effect relationship between the variable whose future values are being forecasted and other related variables or factors. The widely known causal method is called regression analysis, a statistical technique used to develop a mathematical model showing how a set of variables is related. This mathematical relationship can be used to generate forecasts. There are more complex time-series techniques as well, such as ARIMA and Box-Jenkins models. These are heavier duty statistical routines that can cope with data with trends and the seasonality in them.

         Time series models are used in Finance to forecast stock’s performance or interest rate forecast, used in forecasting weather. Time-series methods are probably the simplest methods to deploy and can be quite accurate, particularly over the short term. Various computer software programs are available to find solution using time-series methods.