Business Forecasting Techniques BBABA506 PDF

Business Forecasting Techniques Paper Code: BBABA506 Module 1 Presented By Arindam Roy Assistant Professor, BBA Department Institute of Engineering and Management  Why Forecast? Forecasting is an integral part of...

Business Forecasting Techniques Paper Code: BBABA506 Module 1 Presented By Arindam Roy Assistant Professor, BBA Department Institute of Engineering and Management  Why Forecast? Forecasting is an integral part of the decision making activities of management. An organization establishes goals and objectives, seeks to predict environmental factors, then selects actions that it hopes will result in attainment of these goals and objectives. The need for forecasting is increasing as management attempts to decrease its dependence on chance and becomes more scientific in dealing with its environment. Since each area of an organization is related to all others, a good or bad forecast can affect the entire organization.  Why Forecast? Some of the areas in which forecasting currently plays an important role are:  Time Series and Cross-Sectional Data Generally, two types of data are of interest to the forecaster. The first is data collected at a single point in time, be it an hour, a day, a week, a month, or a quarter. The second is observations of data made over time. Time Series Data Often our historical data will consist of a sequence of observations over time. We call such a sequence a time series. For example, time series monthly sales figures, daily stock prices, weekly interest rates, yearly profits, daily maximum temperatures, annual crop production, and electrocardiograph measurements are all time series. A time series consists of data that are collected, recorded, or observed over successive increments of time In forecasting, we are trying to estimate how the sequence of observations will continue into the future. To make things simple, we will assume that the times of observation are equally spaced. This is not a great restriction because most business series are measured daily, monthly, quarterly, or yearly and so will be equally spaced.  Time Series Data Monthly Australian beer production (megaliters, Ml) from January 1991 to August 1995. The beer data form a time series as they are monthly figures over a period of time.  CROSS-SECTIONAL DATA When all observations are from the same time period, we call them cross-sectional data. The objective is to examine such data and then to extrapolate or extend the revealed relationships to the larger population. Cross-sectional data are observations collected at a single point in time. Examples: i) Drawing a random sample of personnel files to study the circumstances of the employees of a company is one example. ii) Price ($US), mileage (mpg), and country of origin for 45 automobiles from Consumer Reports, April 1990, pp. 235 - 255. A scatter diagram helps us visualize the relationship in case cross-sectional data.  CROSS-SECTIONAL DATA  The automobile data of Table 2-1 are not a time series making time or seasonal plots inappropriate for these data. However, these data are well suited to a scatterplot (see Figure 2-3) such as that of price against mileage.  In Figure 2-3 we have plotted the variable we wish to forecast (price) against one of the explanatory variables (mileage). Each point on the graph represents one type of vehicle. The plot shows the relationship between price and mileage: vehicles with high mileage per gallon are generally cheaper than less fuel-efficient vehicles. (Both price and fuel-efficiency are related to the vehicle and engine size.) The scatterplot helps us visualize the relationship and suggests that a forecasting model must include mileage as an explanatory variable.  Time Series Patterns TREND A trend exists when there is a long-term increase or decrease in the data. It does not have to be linear. Sometimes we will refer to a trend as “changing direction”, when it might go from an increasing trend to a decreasing trend. The trend is the long-term component that represents the growth or decline in the time series over an extended period of time. When data grow or decline over several time periods, a trend pattern exists. Many macroeconomic variables, like the gross national product (GNP), employment, and industrial production exhibit trendlike behavior. Figure 2 shows the long-term growth (trend) of a time series variable (such as housing costs) with data points one year apart. A linear trend line has been drawn to illustrate this growth. Although the variable housing costs have not increased every year, the movement of the variable has been generally upward between periods 1 and 20. Examples of the basic forces that affect and help explain the trend of a series are population growth, price inflation, technological change, consumer preferences, and productivity increases  CYCLICAL COMPONENT  When observations exhibit rises and falls that are not of a fixed period, a cyclical pattern exists. The cyclical component is the wavelike fluctuation around the trend that is usually affected by general economic conditions.  The cyclical component is the wavelike fluctuation around the trend.  A cyclical component, if it exists, typically completes one cycle over several years.  Cyclical fluctuations are often influenced by changes in economic expansions and contractions, commonly referred to as the business cycle.  The sales of products such as automobiles, steel, and major appliances exhibit this type of pattern.  CYCLICAL COMPONENT  Figure 2 also shows a time series with a cyclical component. The cyclical peak at year 9 illustrates an economic expansion and the cyclical valley at year 12 an economic contraction.  SEASONAL COMPONENT A seasonal pattern occurs when a time series is affected by seasonal factors such as the time of the year or the day of the week. Seasonality is always of a fixed and known period. The seasonal component refers to a pattern of change that repeats itself year after year. For a monthly series, the seasonal component measures the variability of the series each January, each February, and so on. For a quarterly series, there are four seasonal elements, one for each quarter. The monthly sales of antidiabetic drugs shows seasonality which is induced partly by the change in the cost of the drugs at the end of the calendar year.  CYCLICAL COMPONENT VS SEASONAL COMPONENT Many people confuse cyclic behaviour with seasonal behaviour, but they are really quite different. If the fluctuations are not of a fixed frequency then they are cyclic; if the frequency is unchanging and associated with some aspect of the calendar, then the pattern is seasonal. In general, the average length of cycles is longer than the length of a seasonal pattern, and the magnitudes of cycles tend to be more variable than the magnitudes of seasonal patterns. Many time series include trend, cycles and seasonality. When choosing a forecasting method, we will first need to identify the time series patterns in the data, and then choose a method that is able to capture the patterns properly. The examples in the following Figure show different combinations of these components. The monthly housing sales (top left) show strong seasonality within each year, as well as some strong cyclic behaviour with a period of about 6–10 years. There is no apparent trend in the data over this period. The US treasury bill contracts (top right) show results from the Chicago market for 100 consecutive trading days in 1981. Here there is no seasonality, but an obvious downward trend. Possibly, if we had a much longer series, we would see that this downward trend is actually part of a long cycle, but when viewed over only 100 days it appears to be a trend. The Australian quarterly electricity production (bottom left) shows a strong increasing trend, with strong seasonality. There is no evidence of any cyclic behaviour here. The daily change in the Google closing stock price (bottom right) has no trend, seasonality or cyclic behaviour. There are random fluctuations which do not appear to be very predictable, and no strong patterns that would help with developing a forecasting model. UNIVARIATE STATISTICS  BIVARIATE STATISTICS Suppose we denote the two variables by X and Y. A statistic which indicates how two variables “co- vary” is called the covariance covariance and is deflned as follows: MEASURING FORECAST ACCURACY MEASURING FORECAST ACCURACY MEASURING FORECAST ACCURACY MEASURING FORECAST ACCURACY AUTOCORRELATION  Sample Questions 1. Explain why forecasting is needed in businesses. 2. From the table below calculate MAD, MSD, Variance, Standard Deviation. Month Number of Units Manufactured Jan 19 Feb 22 March 24 April 30 May 36 June 42 July 48 Aug 53 Sept 57 Oct 65 Nov 72 3. From the above table calculate ME, MAE, MSE, PE, MPE, MAPE. Time Observation Forecast Period 1 139 151.42 2 143 138.25 3 152 142.51 4 128 153.34 5 158 144.67 6 137 152.72 7 149 135.68 8 124 141.83 4. From the above table calculate autocorrelation coefficient for lag 1 and lag2 Time t Month Observed Data Yt Yt-1 Yt-2 1 Jan 123 2 Feb 130 123 3 March 125 130 123 4 April 138 125 130 5 May 145 138 125 6 June 142 145 138 7 July 141 142 145 8 Aug 146 141 142 9 Sept 147 146 141 10 Oct 157 147 146 11 Nov 150 157 147 12 Dec 160 150 157  Business Forecasting Techniques Paper Code: BBABA506 Module 2 Presented By Arindam Roy Assistant Professor, BBA Department Institute of Engineering and Management The additive decomposition is the most appropriate if the magnitude of the seasonal fluctuations, or the variation around the trend-cycle, does not vary with the level of the time series. When the variation in the seasonal pattern, or the variation around the trend-cycle, appears to be proportional to the level of the time series, then a multiplicative decomposition is more appropriate. Multiplicative decompositions are common with economic time series.  The method of simple averages uses the mean of all the data to forecast. What if the analyst is more concerned with recent observations? A constant number of data points can be specified at the outset and a mean computed for the most recent observations. One way to modify the influence of past data on the mean-as-a-forecast is to specify at the outset just how many past observations will be included in a mean. The term “moving average" is used to describe this procedure because as each new observation becomes available, a new average can be computed by dropping the oldest observation and including the newest one. This moving average will then be the forecast for the next period. Note that the number of data points in each average remains constant and includes the most recent observations. Yt = the actual value at period t k = the number of terms in the moving average bt ≣Tt m ≣p  Equation 15 is very similar to the equation for simple exponential smoothing, except that a term (Tt) has been incorporated to properly update the level when a trend exists. That is, the current level (Lt)is calculated by taking a weighted average of two estimates of level—one estimate is given by the current observation (Yt) , and the other estimate is given by adding the previous trend (Tt-1) to the previously smoothed level (Lt-1). If there is no trend in the data, there is no need for the term Tt-1 in Equation 15, effectively reducing it to Equation 13.There is also no need for Equation 16.  A second smoothing constant, β, is used to create the trend estimate. Equation 16 shows that the current trend (Tt) is a weighted average (with weights β and 1- β) of two trend estimates— one estimate is given by the change in level from time (t -1) to t (Lt – Lt-1) , and the other estimate is the previously smoothed trend Tt-1. Equation 16 is similar to Equation 15, except that the smoothing is done for the trend rather than the actual data.  Equation 17 shows the forecast for p/m periods into the future. For a forecast made at time t, the current trend estimate (Tt) is multiplied by the number of periods to be forecast (p/m), and then the product is added to the current level (Lt). Note that the forecasts for future periods lie along a straight line with slope Tt and intercept Lt L1 = Y1 = 143 b1 = Y2 – Y1 = 152 -143= 9 F 1 + 1 = L1 + b1 (1) = 143 + 9 = 152 L2 = α Y2 + (1- α) (L1 + b1 ) b2 = β(L2 - L1) + ( 1 – β) b1 F 2 + 1 = L2 + b2 (1) S= 4  SAMPLE QUESTIONS 1. Using the single series 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20, compute a forecast for period 11 using the method of single exponential smoothing. Take α = 0.3 2. Using the single series 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20, compute a forecast for period 11 using the Holt’s method of linear exponential smoothing. Take α = 0.3 and β = 0.1 3. What will the forecast be for December for exponential smoothing with α value of 0.1? Month Time Period Observed Values Yt Jan 1 200.00 Feb 2 135.00 March 3 195.00 April 4 197.50 May 5 310.00 June 6 175.00 July 7 155.00 Aug 8 130.00 Sept 9 220.00 Oct 10 277.5 Nov 11 235.00 Dec 12 4. From the given Table data, what will the forecast be for December using a 3 month moving average? Month Time Period Observed Values Yt Jan 1 200.00 Feb 2 135.00 March 3 195.00 April 4 197.50 May 5 310.00 June 6 175.00 July 7 155.00 Aug 8 130.00 Sept 9 220.00 Oct 10 277.5 Nov 11 235.00 Dec 12  Business Forecasting Techniques Paper Code: BBABA506 Module 3 Presented By Arindam Roy Assistant Professor, BBA Department Institute of Engineering and Management  SAMPLE QUESTIONS 1. Calculate the variance of AR (2), the autoregressive process of order two. 2. Calculate the covariance of lag1 of AR (2), the autoregressive process of order two. 3. Calculate the covariance of lag2 of AR (2), the autoregressive process of order two. 4. Calculate the variance of MA (2), the moving average process of order two. 5. Calculate the covariance of lag1 of MA (2), the moving average process of order two. 6. Calculate the covariance of lag2 of MA (2), the moving average process of order two. 7. Analyze why the Mean of the Random Walk without Drift does not vary with time but the Variance increases with time. 8. Analyze why the Mean and the Variance of the Random Walk with Drift increase with time. 9. Explain Box-Pierce Test.  SAMPLE QUESTIONS 1. Calculate the variance of ARMA (1, 1), the mixed autoregressive moving average process of order (1,1) 2. Calculate the covariance of lag1 of the ARMA (1, 1), the mixed autoregressive moving average process of order (1,2). 3. Calculate the covariance of lag1 of the ARMA (1, 2), the mixed autoregressive moving average process of order (1,2). 4. Calculate the covariance of lag2 of the ARMA (1, 2), the mixed autoregressive moving average process of order (1,2). 5. Calculate the variance and covariances of ARMA (2, 1), the mixed autoregressive moving average process of order (2,1). 6. Write the equation of ARIMA (1, 1, 1) in terms of backshift operator. 7. Write the equation of ARIMA (2, 1, 1) in terms of backshift operator.