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February 21, 2008

Time-series methods of forecasting

Filed under: Business management — Jagdish Hiray @ 10:19 pm
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         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.  



  1. Good explanation however it is more easy to understand if some more example is taken with this … in case of Three-period moving averages weight give as .4,.3,.2…but is is not explanined anywhere why it is not .3,.2,.1….
    This is quite a helpful explanation thanks for help

    Comment by Pankaj — March 30, 2008 @ 9:44 am | Reply

  2. Thank you Pankaj,
    Weights .4,.3,.2 are taken for example and does not have any specific meaning or logic.

    Comment by Jagdish Hiray — March 30, 2008 @ 8:41 pm | Reply

  3. To understand time series forecating,you gave a very straight forward report. could you help me in analysisng a graph made from the trend and seasonal time series forcasting where moving averages are used for forecasting. As well how to interpret a table of average seasonal variation drawn from trend and seasonal time series forecasting.

    Comment by mitti — April 10, 2008 @ 6:05 am | Reply


    Comment by MONALISA CHAKRABORTY — April 11, 2008 @ 9:18 pm | Reply

  5. Habituation says : I absolutely agree with this !

    Comment by habituation — June 4, 2008 @ 1:42 am | Reply

  6. Somehow i missed the point. Probably lost in translation 🙂 Anyway … nice blog to visit.

    cheers, Percipient

    Comment by Percipient — June 19, 2008 @ 4:22 am | Reply

  7. Perfect answer, it made me get the concept so clear, yet a friend had discouraged me that forecasting models are not easy. By the way, could you be having materials on Waiting lines models, possibly with some examples. I wouldn’t mind if you email. Good work.

    Comment by Justus M. — August 14, 2009 @ 4:44 am | Reply

  8. I think theer is an error in the three period moving average example – I think the forcast should rather be 1.25.

    Please mail me at the above address and clear my confusion…

    Comment by S N Roy — December 21, 2009 @ 3:03 am | Reply

  9. Dear Sir,
    I read the paper and If possible please send me other details related to time series method for forecasting which is my Ph.D. topic.

    Thanking you

    Comment by VIJAY DEV — January 13, 2010 @ 10:15 pm | Reply

  10. This is a good explanation i am impressed. however I would like to know more on what could be the difference between causal and time-series based data analysis and forecasting methods.

    Comment by Martha Kaunapawa Tsheehama — May 12, 2010 @ 7:42 am | Reply

  11. completely helpful,my research was a success because of th document,would appreciate to get more business related blocs in my e-mails,thanks

    Comment by Paul Mnetwa — September 22, 2010 @ 5:35 pm | Reply

  12. Dear sir,

    please help me out. does this analysis can be used in Churn management and crm

    Comment by faizal — April 19, 2011 @ 9:22 am | Reply

  13. i want to know the techniques for forcasting the sensex

    Comment by mayuresh — September 20, 2011 @ 8:59 am | Reply

  14. please i want you to send me some important topic in time series that can help me in university project.

    Comment by okeje peter — March 22, 2012 @ 6:00 am | Reply

  15. I’ve learn a few excellent stuff here. Certainly value bookmarking for revisiting. I wonder how a lot attempt you set to create this type of great informative site.

    Comment by Katherina — June 20, 2013 @ 3:59 am | Reply

  16. We absolutely love your blog and find many of your post’s to be what precisely I’m looking for.
    Would you offer guest writers to write content for you personally?
    I wouldn’t mind composing a post or elaborating on a number of the subjects you write about here. Again, awesome web site!

    Comment by best mba in finance — July 30, 2013 @ 5:57 pm | Reply

  17. I was wondering if you ever considered changing the page layout of your website?
    Its very well written; I love what youve got to say. But maybe you
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    Comment by Ge finance — August 6, 2013 @ 11:25 am | Reply

  18. Thnx

    Comment by Kellz — September 25, 2013 @ 5:47 pm | Reply

  19. Dear Sir, I need help on the following – examples of application of forecasting in industries.

    Comment by Albert — June 27, 2014 @ 1:51 am | Reply

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