TSTA602 Week 10● Time Series○ Data Types○ Decomposition○ Smoothing■ Moving Average■ Exponential Smooth○ AutoregressionData Types● Data TypesData Types● Data Types○ cross-sectionalData Types● Data Types○ cross-sectional■ data collected at a single pointData Types● Data Types○ cross-sectional■ data collected at a single point■ group of individualsData Types● Data Types○ cross-sectional■ data collected at a single point■ group of individuals■ (e.g.) closing price of group of stocksData Types● Data Types○ cross-sectional■ data collected at a single point■ group of individuals■ (e.g.) closing price of group of stocks○ time seriesData Types● Data Types○ cross-sectional■ data collected at a single point■ group of individuals■ (e.g.) closing price of group of stocks○ time series■ data collected at many different point of timeData Types● Data Types○ cross-sectional■ data collected at a single point■ group of individuals■ (e.g.) closing price of group of stocks○ time series■ data collected at many different point of time■ individualData Types● Data Types○ cross-sectional■ data collected at a single point■ group of individuals■ (e.g.) closing price of group of stocks○ time series■ data collected at many different point of time■ individual■ (e.g.) closing price of stock XDecompositionDecompositionTrend: a smooth, slowlymeandering patternDecompositionTrend: a smooth, slowlymeandering patternSeasonal: cyclic oscillationthat follow the calendar(every fixed period).DecompositionTrend: a smooth, slowlymeandering patternSeasonal: cyclic oscillationthat follow the calendar(every fixed period).Irregular: random variationthat is unpredictable from onetime to the next.DecompositionTrend: a smooth, slowlymeandering patternSeasonal: cyclic oscillationthat follow the calendar(every fixed period).Irregular: random variationthat is unpredictable from onetime to the next.Smoothing– trend are easier to see byremoving seasonal andirregular components.DecompositionTrend: a smooth, slowlymeandering patternSeasonal: cyclic oscillationthat follow the calendar(every fixed period).Irregular: random variationthat is unpredictable from onetime to the next.Smoothing– trend are easier to see byremoving seasonal andirregular components.Forecasting– predicting future valuesbased known observationsSmoothingSmoothingSmoothingSmoothingMoving Average– using weighted averageof adjacent values of atime seriesSmoothingSmoothingMoving Average– using weighted averageof adjacent values of atime seriesExponential Smoothing– exponential weighted movingaverage– mathematically, can be writtenas an equivalent formula.Moving Average(Ken pp 616 – 617) The shipments (in millions of dollars) for electric lighting equipment over a 12-months period.a) Forecasting monthly for April, May, June, July,August, September, October, November,December shipments by using a 3-monthsmoving average.b) Find the corresponding forecasting error from a). MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averagea) Forecasting monthly for April, May, June, July, August, September, October, November, December shipments byusing a 3-months moving average. MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averagea) Forecasting monthly for April, May, June, July, August, September, October, November, December shipments byusing a 3-months moving average. MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averagea) Forecasting monthly for April, May, June, July, August, September, October, November, December shipments byusing a 3-months moving average. MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averagea) Forecasting monthly for April, May, June, July, August, September, October, November, December shipments byusing a 3-months moving average. MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averagea) Forecasting monthly for April, May, June, July, August, September, October, November, December shipments byusing a 3-months moving average. MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averagea) Forecasting monthly for April, May, June, July, August, September, October, November, December shipments byusing a 3-months moving average. MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averagea) Forecasting monthly for April, May, June, July, August, September, October, November, December shipments byusing a 3-months moving average. MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averagea) Forecasting monthly for April, May, June, July, August, September, October, November, December shipments byusing a 3-months moving average. MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averagea) Forecasting monthly for April, May, June, July, August, September, October, November, December shipments byusing a 3-months moving average. MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averagea) Forecasting monthly for April, May, June, July, August, September, October, November, December shipments byusing a 3-months moving average. MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving AverageMoving Averageb) Find the corresponding forecasting error from a). MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averageb) Find the corresponding forecasting error from a). MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averageb) Find the corresponding forecasting error from a). MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averageb) Find the corresponding forecasting error from a). MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averageb) Find the corresponding forecasting error from a). MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averageb) Find the corresponding forecasting error from a). MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averageb) Find the corresponding forecasting error from a). MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averageb) Find the corresponding forecasting error from a). MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Moving Averageb) Find the corresponding forecasting error from a). MonthShipmentsMonthShipmentsJan1056Jul1110Feb1345Aug1334Mar1381Sep1416Apr1191Oct1282May1259Nov1341Jun1361Dec1382 Exponential Smoothing(Dr Liu Lecture Notes) The pricing of new housing units (denoted by X) are given here. Using exponential smoothing toforecast the values for 1994, 1995, and 1996 and find the corresponding forecasts error . YearHousing Units (x)19911014199212001993128819941457199513541996147719971474 Exponential Smoothing(Dr Liu Lecture Notes) The pricing of new housing units (denoted by X) are given here. Using exponential smoothing toforecast the values for 1994, 1995, and 1996 and find the corresponding forecasts error . YearHousing Units (x)19911014199212001993128819941457199513541996147719971474 Exponential Smoothing(Dr Liu Lecture Notes) The pricing of new housing units (denoted by X) are given here. Using exponential smoothing toforecast the values for 1994, 1995, and 1996 and find the corresponding forecasts error . YearHousing Units (x)19911014199212001993128819941457199513541996147719971474 Exponential Smoothing(Dr Liu Lecture Notes) The pricing of new housing units (denoted by X) are given here. Using exponential smoothing toforecast the values for 1994, 1995, and 1996 and find the corresponding forecasts error . YearHousing Units (x)19911014199212001993128819941457199513541996147719971474 Exponential Smoothing(Dr Liu Lecture Notes) The pricing of new housing units (denoted by X) are given here. Using exponential smoothing toforecast the values for 1994, 1995, and 1996 and find the corresponding forecasts error . YearHousing Units (x)19911014199212001993128819941457199513541996147719971474 Exponential Smoothing(Dr Liu Lecture Notes) The pricing of new housing units (denoted by X) are given here. Using exponential smoothing toforecast the values for 1994, 1995, and 1996 and find the corresponding forecasts error . YearHousing Units (x)19911014199212001993128819941457199513541996147719971474 Exponential Smoothing(Dr Liu Lecture Notes) The pricing of new housing units (denoted by X) are given here. Using exponential smoothing toforecast the values for 1994, 1995, and 1996 and find the corresponding forecasts error . YearHousing Units (x)19911014199212001993128819941457199513541996147719971474 Exponential Smoothing(Dr Liu Lecture Notes) The pricing of new housing units (denoted by X) are given here. Using exponential smoothing toforecast the values for 1994, 1995, and 1996 and find the corresponding forecasts error . YearHousing Units (x)19911014199212001993128819941457199513541996147719971474 Exponential Smoothing(Dr Liu Lecture Notes) The pricing of new housing units (denoted by X) are given here. Using exponential smoothing toforecast the values for 1994, 1995, and 1996 and find the corresponding forecasts error . YearHousing Units (x)19911014199212001993128819941457199513541996147719971474 Exponential Smoothing(Dr Liu Lecture Notes) The pricing of new housing units (denoted by X) are given here. Using exponential smoothing toforecast the values for 1994, 1995, and 1996 and find the corresponding forecasts error . YearHousing Units (x)19911014199212001993128819941457199513541996147719971474 Autoregression● Smoothing is applied to forecast short term value.Autoregression● Smoothing is applied to forecast short term value.● For long term horizon forecasting, regression is often used.Autoregression● Smoothing is applied to forecast short term value.● For long term horizon forecasting, regression is often used.● For time series data, there is often some correlation between responses at differenttime.Autoregression● Smoothing is applied to forecast short term value.● For long term horizon forecasting, regression is often used.● For time series data, there is often some correlation between responses at differenttime.● Autoregression models responses by using prior response (called lagged variable) asfactor.AutoregressionAutoregressionAutoregressionAR(2): second-order autoregressionAutoregression(Dr Liu Lecture Notes) Predict the export for 2010 YearReal GDPYearReal GDP200072.1200584.368200174.445200686.135200277.66200786.492200379.787200886.376200483.723200986.862 Autoregression(Dr Liu Lecture Notes) Predict the export for 2010 YearReal GDPYearReal GDP200072.1200584.368200174.445200686.135200277.66200786.492200379.787200886.376200483.723200986.862 Call: ar.ols(x = week10_data2$GDP, order.max = 2, intercept =TRUE, demean = TRUE)Coefficients120.51180.1895Intercept: 26.5 (6.357)Order selected 2 sigma^2 estimated as 0.551 Autoregression(Dr Liu Lecture Notes) Predict the export for 2010 YearReal GDPYearReal GDP200072.1200584.368200174.445200686.135200277.66200786.492200379.787200886.376200483.723200986.862 Call: ar.ols(x = week10_data2$GDP, order.max = 2, intercept =TRUE, demean = TRUE)Coefficients120.51180.1895Intercept: 26.5 (6.357)Order selected 2 sigma^2 estimated as 0.551 Autoregression(Dr Liu Lecture Notes) Predict the export for 2010 YearReal GDPYearReal GDP200072.1200584.368200174.445200686.135200277.66200786.492200379.787200886.376200483.723200986.862 Call: ar.ols(x = week10_data2$GDP, order.max = 2, intercept =TRUE, demean = TRUE)Coefficients120.51180.1895Intercept: 26.5 (6.357)Order selected 2 sigma^2 estimated as 0.551 Autoregression(Dr Liu Lecture Notes) Predict the export for 2010 YearReal GDPYearReal GDP200072.1200584.368200174.445200686.135200277.66200786.492200379.787200886.376200483.723200986.862 Call: ar.ols(x = week10_data2$GDP, order.max = 2, intercept =TRUE, demean = TRUE)Coefficients120.51180.1895Intercept: 26.5 (6.357)Order selected 2 sigma^2 estimated as 0.551 Autoregression(Dr Liu Lecture Notes) Predict the export for 2010 YearReal GDPYearReal GDP200072.1200584.368200174.445200686.135200277.66200786.492200379.787200886.376200483.723200986.862 Call: ar.ols(x = week10_data2$GDP, order.max = 2, intercept =TRUE, demean = TRUE)Coefficients120.51180.1895Intercept: 26.5 (6.357)Order selected 2 sigma^2 estimated as 0.551 Reference● Robert Stine and Dean Foster, Statistics for Business, 3rd ed, 2017● Dr David Liu, TSTA401 Session 2, 2019, Lecture Notes● Ken Black, Business Statistics, 8th ed., 2014, John Wiley & Sons, Inc.● Time Series Data vs Cross-Sectional Datahttps://analystnotes.com/cfa-study-notes-distinguish-between-time-series-and-cross-sectional-data.html
