SMOOTHIE: Interactive Time--Series Analysis by Richard S. Barr and James Collins SMOOTHIE is an interactive program for time--series data that permits the application of several forecasting models to a set of data. The user can apply single and double exponential smoothing, moving average, trend, arithmetic mean, and complete decomposition methods to a given data series. Running SMOOTHIE Prepare a data file using a text editor and the instructions below. To execute the program, type the following at the DOS prompt: SMOOTHIE filename where filename is the name of the data file. If filename is omitted, operating instructions are displayed. Data File Organization The data file contains a set of time--series data in free format. That is, it consists of a series of observed values for a single variable, taken at uniform time intervals, given in chronological order, and separated by blanks or on separate lines. The following example file will be used below to illustrate the use of the program, and is assumed to be in the file named MYFILE. 13.1 12 15.8 11.4 14 15.3 17.6 13 15.2 16.4 19.2 14.7 15.6 15.5 17.2 16.7 16.8 16.5 17.4 14.4 17.0 19.4 19.2 16.7 There are 25 observations of a variable, given in time--series order. Program Operation and Report Interpretation In the sections that follow, user input will be shown in underlined boldface. To process the above data file, we enter: SMOOTHIE myfile The initial screen displays: *** SMOOTHIE: INTERACTIVE TIME--SERIES FORECASTING *** by Richard S. Barr and Jim Collins Processing data file smoothie.dat 24 observations were read How many observations to use in the mean error calculation (enter 0 for the maximum possible)? 5 The user is asked to enter the number of observations to be used in calculating cumulative error values, such as mean squared error (MSE). Since the models result in varying numbers of historical error terms, one may wish to use a subset in computing cumulatives, if the values are to be compared across models. We have asked that only the most recent five error values be used. *** SMOOTHIE: INTERACTIVE TIME--SERIES FORECASTING *** The following forecasting models are available: Moving average Exponential smoothing (single) Smoothing with trend (double) Trend Arithmetic mean Decomposition Select model by typing the first letter, or ESC to quit: Any of the six models listed may be applied to the dataset. A model is selected by typing its first letter, such as M for moving average. Each model type results in a different forecast methodology and set of reports. The output for each model as applied to our dataset is given below. NOTE: To prevent reports from scrolling off of the screen before viewing by the user, output pauses at the end of each full screen. This condition is indicated by a & symbol, and the user may press any key to continue. M, Moving Average Forecasts Moving average forecasting is selected at the main menu by the M key. The user is then asked to enter the number of periods to be used in the averaging process. In our example, we will perform a 3--period moving average. *** MOVING AVERAGE METHOD *** Number of periods for your moving average: 3 *** SUMMARY REPORT *** Period Actual Forecast Error Number Observn for Next (Forecast-- Period Actual) ------ -------- -------- -------- 1 13.100 2 12.000 3 15.800 13.633 4 11.400 13.067 --2.233 5 14.000 13.733 0.933 6 15.300 13.567 1.567 7 17.600 15.633 4.033 8 13.000 15.300 --2.633 9 15.200 15.267 --0.100 10 16.400 14.867 1.133 11 19.200 16.933 4.333 12 14.700 16.767 --2.233 13 15.600 16.500 --1.167 14 15.500 15.267 --1.000 15 17.200 16.100 1.933 16 16.700 16.467 0.600 17 16.800 16.900 0.333 18 16.500 16.667 --0.400 19 17.400 16.900 0.733 20 14.400 16.100 --2.500 21 17.000 16.267 0.900 22 19.400 16.933 3.133 23 19.200 18.533 2.267 24 16.700 18.433 --1.833 *** FORECAST ERROR MEASURES *** Specified Maximum Number of periods 5 21 Mean squared error (MSE) 5.075 4.249 Mean absolute error (MAD) 2.127 1.714 Mean absolute pct error (MAPE) 12.318 10.666 Mean error/Forecast bias 0.393 0.371 E, Single Exponential Smoothing When E" is chosen from the main menu, and a smoothing constant (a) of 0.5 is selected, the following reports result. *** EXPONENTIAL SMOOTHING (SINGLE) *** What smoothing constant do you wish to use (0 < a < 1)? 0.5 *** SUMMARY REPORT *** Period Actual Forecast Error Number Observn for Next (Forecast-- Period Actual) ------ -------- -------- -------- 1 13.100 13.100 2 12.000 12.550 --1.100 3 15.800 14.175 3.250 4 11.400 12.788 --2.775 5 14.000 13.394 1.212 6 15.300 14.347 1.906 7 17.600 15.973 3.253 8 13.000 14.487 --2.973 9 15.200 14.843 0.713 10 16.400 15.622 1.557 11 19.200 17.411 3.578 12 14.700 16.055 --2.711 13 15.600 15.828 --0.455 14 15.500 15.664 --0.328 15 17.200 16.432 1.536 16 16.700 16.566 0.268 17 16.800 16.683 0.234 18 16.500 16.591 --0.183 19 17.400 16.996 0.809 20 14.400 15.698 --2.596 21 17.000 16.349 1.302 22 19.400 17.874 3.051 23 19.200 18.537 1.326 24 16.700 17.619 --1.837 *** FORECAST ERROR MEASURES *** Specified Maximum Number of periods 5 23 Mean squared error (MSE) 4.575 4.063 Mean absolute error (MAD) 2.022 1.694 Mean absolute pct error (MAPE) 11.864 10.863 Mean error/Forecast bias 0.249 0.393 S, Smoothing with Trend (Double) Double exponential smoothing uses both a smoothing constant, a, but a trend emphasis constant, b. Both values are between 0 and 1. *** EXPONENTIAL SMOOTHING WITH TREND (DOUBLE) *** What DATA smoothing constant do you wish to use (0 < a <1)? 0.5 What TREND smoothing constant do you wish to use (0 < b <1)? 0.6 Forecast using 18.340528 + 0.094073 * (number of periods beyond 24) *** SUMMARY REPORT *** Period Actual Forecast Error Number Observn for Next (Forecast-- Period Actual) ------ -------- -------- -------- 1 13.100 13.100 2 12.000 12.220 --1.100 3 15.800 14.754 3.580 4 11.400 12.815 --3.354 5 14.000 13.501 1.185 6 15.300 15.034 1.799 7 17.600 17.720 2.566 8 13.000 15.347 --4.720 9 15.200 15.217 --0.147 10 16.400 16.106 1.183 11 19.200 18.879 3.094 12 14.700 16.762 --4.179 13 15.600 15.805 --1.162 14 15.500 15.185 --0.305 15 17.200 16.329 2.015 16 16.700 16.763 0.371 17 16.800 17.041 0.037 18 16.500 16.867 --0.541 19 17.400 17.391 0.533 20 14.400 15.255 --2.991 21 17.000 16.011 1.745 22 19.400 18.605 3.389 23 19.200 19.981 0.595 24 16.700 18.435 --3.281 *** FORECAST ERROR MEASURES *** Specified Maximum Number of periods 5 23 Mean squared error (MSE) 6.919 5.568 Mean absolute error (MAD) 2.400 1.907 Mean absolute pct error (MAPE) 14.250 12.445 Mean error/Forecast bias --0.109 0.014 T, Trend Forecasting with a trend line only involved fitting a simple regression line to the observed points, using the period number as the independent variable. *** LEAST--SQUARES TREND LINE *** Trend equation: T = 13.352174 + 0.198826 * t Sample coefficient of determination (R--squared) = 0.433809 *** SUMMARY REPORT *** Period Actual Forecast Error Number Observn for Next (Forecast-- Period Actual) ------ -------- -------- -------- 1 13.100 13.100 2 12.000 10.900 --1.100 3 15.800 16.333 4.900 4 11.400 12.750 --4.933 5 14.000 13.620 1.250 6 15.300 14.860 1.680 7 17.600 16.786 2.740 8 13.000 15.546 --3.786 9 15.200 15.731 --0.346 10 16.400 16.313 0.669 11 19.200 17.715 2.887 12 14.700 17.192 --3.015 13 15.600 17.069 --1.592 14 15.500 16.935 --1.569 15 17.200 17.275 0.265 16 16.700 17.408 --0.575 17 16.800 17.528 --0.608 18 16.500 17.551 --1.028 19 17.400 17.753 --0.151 20 14.400 17.313 --3.353 21 17.000 17.437 --0.313 22 19.400 17.973 1.963 23 19.200 18.389 1.227 24 16.700 18.323 --1.689 *** FORECAST ERROR MEASURES *** Specified Maximum Number of periods 5 23 Mean squared error (MSE) 3.910 5.225 Mean absolute error (MAD) 1.709 1.810 Mean absolute pct error (MAPE) 10.350 12.075 Mean error/Forecast bias --0.433 --0.282 A, Arithmetic Mean The average of all previous observations can be used as a forecast, as follows. *** ARITHMETIC MEAN AS A FORECAST *** The overall mean of Y is 15.837500 *** SUMMARY REPORT *** Period Actual Forecast Error Number Observn for Next (Forecast-- Period Actual) ------ -------- -------- -------- 1 13.100 13.100 2 12.000 12.550 --1.100 3 15.800 13.633 3.250 4 11.400 13.075 --2.233 5 14.000 13.260 0.925 6 15.300 13.600 2.040 7 17.600 14.171 4.000 8 13.000 14.025 --1.171 9 15.200 14.156 1.175 10 16.400 14.380 2.244 11 19.200 14.818 4.820 12 14.700 14.808 --0.118 13 15.600 14.869 0.792 14 15.500 14.914 0.631 15 17.200 15.067 2.286 16 16.700 15.169 1.633 17 16.800 15.265 1.631 18 16.500 15.333 1.235 19 17.400 15.442 2.067 20 14.400 15.390 --1.042 21 17.000 15.467 1.610 22 19.400 15.645 3.933 23 19.200 15.800 3.555 24 16.700 15.837 0.900 *** FORECAST ERROR MEASURES *** Specified Maximum Number of periods 5 23 Mean squared error (MSE) 6.519 5.164 Mean absolute error (MAD) 2.208 1.930 Mean absolute pct error (MAPE 12.177 11.761 Mean error/Forecast bias 1.791 1.437 D, Decomposition Time--series decomposition separates the observations into four components: trend, seasonal, cyclical, and irregular/random. The multiplicative model is of the form: . The user can then assemble a forecast for a future period by estimating its cyclical index (a value of 1.0 can be used to ignore this component). A detailed historical decomposition report is available as a use option. For computing the seasonal component, the user must indicate whether the observations are monthly or quarterly data values. The sample dataset is based on quarterly observations. *** TIME SERIES DECOMPOSITION *** Is the data monthly or quarterly (M/Q)? Q Quarterly Trend equation: T = 13.657547 + 0.178496 * Period Sample coefficient of determination (R--squared) = 0.826790 Season Seasonal Index ------ -------------- Quarter 1 0.9794 Quarter 2 1.0167 Quarter 3 1.1347 Quarter 4 0.8693 Modified means used in 4 seasonal index calculations Mean irregular index = 1.005263 Do you want a detailed report (Y/N)? Y D E C O M P O S I T I O N S U M M A R Y Period Actual Trend Seasonal Cyclical Forecast Error 3 15.800 14.193 1.135 0.929 16.105 --0.305 4 11.400 14.372 0.869 0.954 12.493 --1.093 ------------------------------------------------------------------ 5 14.000 14.550 0.979 0.986 14.250 --0.250 6 15.300 14.729 1.017 1.003 14.974 0.326 7 17.600 14.907 1.135 1.015 16.915 0.685 8 13.000 15.086 0.869 1.022 13.113 --0.113 ------------------------------------------------------------------ 9 15.200 15.264 0.979 1.032 14.949 0.251 10 16.400 15.443 1.017 1.047 15.700 0.700 11 19.200 15.621 1.135 1.051 17.725 1.475 12 14.700 15.800 0.869 1.036 13.734 0.966 ------------------------------------------------------------------ 13 15.600 15.978 0.979 1.001 15.648 --0.048 14 15.500 16.156 1.017 0.990 16.426 --0.926 15 17.200 16.335 1.135 1.004 18.535 --1.335 16 16.700 16.513 0.869 1.010 14.355 2.345 ------------------------------------------------------------------ 17 16.800 16.692 0.979 1.008 16.348 0.452 18 16.500 16.870 1.017 0.982 17.152 --0.652 19 17.400 17.049 1.135 0.956 19.345 --1.945 20 14.400 17.227 0.869 0.969 14.975 --0.575 ------------------------------------------------------------------ 21 17.000 17.406 0.979 0.992 17.047 --0.047 22 19.400 17.584 1.017 1.012 17.878 1.522 Forecast based on trend and seasonal only Mean squared error for periods 3 through 22 = 1.040293 *** INTERACTIVE FORECASTING *** Period to forecast or 0? 30 Cyclical index to use or 1 to ignore? 1 Forecast = Trend * Seasonal Index * Cyclical Index 19.329 = 19.012 * 1.017 * 1.000 Period to forecast or 0? 0 Exiting SMOOTHIE To exit the system, press the Escape key from the main menu.