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Times Series Introduction
- 1. Times Series Introduction Moving Averages • Used to smooth the times series such that the trend can be more easily determined • Simple n-day moving average is calculated by taking the successive averages of n consecutive values in the time series
- 2. • Exponential moving average is a weighted average giving more priority to values observed later in the time series Line Graph1) Generate a line graph to viualize your time-series data. Place the time intervals on the horizontal axisTime IndexQuarterSales1Q1732Q2903Q31214Q4985Q1696Q2927Q31 458Q41079Q18610Q211111Q315712Q412213Q18814Q21092) How might you describe the TREND of the time-series? (upward or downward)15Q3159Reading the graph from left to right, this time series looks as if the data is trending upward16Q4131 Sales Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 73 90 121 98 69 92 145 107 86 111 157 122 88 109 159 131 Quarters Sales
- 3. Trendline3) Use Excel to add a trendline to the time-series chartTime IndexQuarterSales1Q1732Q2903Q31214Q4985Q1696Q2927Q31 458Q41079Q18610Q211111Q315712Q412213Q18814Q21094) Upon visual inspection, which trendline appears to be most resprentative of the time-series data?15Q3159For this chart, the Moving Averages, with period 2, trend line appears to be most representative16Q4131 Sales Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 73 90 121 98 69 92 145 107 86 111 157 122 88 109 159 131 Quarters Sales Exponential Smoothing5) Use exponential smoothing (Data .. Data Analysis … Exponential Smoothing) to smooth out the peaks and vallies in the plot to better see the trendTime IndexQuarterSalesUse dampening factors = .3, .6, and .9 to generate 3 charts1Q1732Q290see image below3Q31214Q4985Q1696Q2927Q31458Q41079Q18610Q2111 11Q315712Q412213Q18814Q210915Q315916Q4131 ExponentialSmoothing2Time IndexQuarterSales0.30.60.91Q173ERROR:#N/AERROR:#N/AE RROR:#N/A2Q2907373733Q312184.979.874.74Q498110.1796. 2879.335Q169101.65196.96881.1976Q29278.795385.780879.97 737Q314588.0385988.2684881.179578Q4107127.911577110.96 108887.5616139Q186113.2734731109.376652889.505451710Q2 11194.18204193100.0259916889.1549065311Q3157105.954612 579104.41559500891.33941587712Q4122141.6863837737125.4
- 4. 49357004897.905474289313Q188127.9059151321124.06961420 29100.31492686046) Discuss what happens in the chart as the dampening factor increases?14Q210999.9717745396109.641768521799.08343417 4315Q3159106.2915323619109.385061113100.0750907569) Use of which dampening factor has aided in your ability to see the time-series trend16Q4131143.1874597086129.2310366678105.9675816812 .3 dampening factor Actual 73 90 121 98 69 92 145 107 86 111 157 122 88 109 159 131 Forecast #N/A 73 84.899999999999991 110.16999999999999 101.65099999999998 78.795299999999997 88.038589999999985 127.91157699999999 113.27347309999999 94.182041929999997 105.95461257899998 141.68638377369999 127.90591513210998 99.971774539632989 106.29153236188989 143.18745970856696 Time Point Sales .6 Dampening Factor Actual 73 90 121 98 69 92 145 107 86 111 157 122 88 109 159 131 Forecast #N/A 73 79.8 96.28 96.968000000000004 85.780799999999999 88.268480000000011 110.961088 109.37665280000002 100.02599168 104.415595008 125.44935700479999 124.06961420287999 109.641768521728 109.38506111303678 129.23103666782208 Time Point Sales .9 Dampening Factor Actual 73 90 121 98 69 92 145 107 86 111 157 122 88 109 159 131 Forecast #N/A 73 74.7 79.330000000000013 81.197000000000017 79.977300000000028 81.179570000000027
- 5. 87.561613000000023 89.505451700000023 89.154906530000019 91.339415877000022 97.905474289300031 100.31492686037004 99.083434174333036 100.07509075689974 105.96758168120978 Time Point Sales Seasonality8) Do you notice any SEASONAL effects? (predictable fluctuations (systematic) that occur during the same month (or quarters, etc ..)Time IndexQuarterSales1Q1732Q2903Q31214Q4985Q1696Q2927Q31 458Q41079Q18610Q211111Q315712Q412213Q18814Q210915 Q315916Q4131There appears to be a seasonal effect present in the graph. The graph fluctuates in a predictable patternfrom quarter 1 to quarter 4 or yearly. Sales start low in quarter 1 and increases to a peak in Quarter 3then decreases in Quarter 4 to near quarter 2 sales levels but not quite as low as sales posted for quarter 1.That is, it is expected that quarter 1 sales will be the lowest for the year and quarter 3 sales will be highest. Sales Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 73 90 121 98 69 92 145 107 86 111 157 122 88 109 159 131 Quarters Sales Forecast Sheet9) Use Excel to Generate a Forecast sheet (Data … Forecast Menu … Forecast Sheet…Options) to predict valuse for the next 5 time intervalsUse the Time Period colum for the Timeline Range window (see image below)Time IndexQuarterSales1Q1732Q2903Q31214Q4985Q1696Q2927Q31 458Q41079Q18610Q211111Q315712Q412213Q18814Q210915 Q315916Q4131
- 6. Enter the last Excel row number in your dataset Add 5 to your Forecast Start value Uncheck this box Time period column Measurement Data Forecast Sheet 2TimelineValuesForecast17310) List the next 5 values forecast290312149856969271458107986101111115 7121221388 14109151591613113117102.94275968218126.30701097741916 8.690769202820138.178750426421112.411840624TimelineFore cast17102.94275968218126.307010977419168.69076920282013 8.178750426421112.411840624 Values 73 90 121 98 69 92 145 107 86 111 157 122 88 109 159 131 Forecast 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 131 102.94275968196206 126.30701097740565 168.69076920283931 138.17875042637019 112.41184062403286 Moving AverageTime IndexQuarterSalesif there is no apparent trend, then smoothing with moving averages could be a next step to help identify the long term trend1Q173used to reduce the random fluctuation2Q290Simple moving average (SMA) is an arithmetic average of values at and near a particular time period - each observation is weighted equally3Q3121compute means for a sequence of L observed values4Q498assumes observations which are nearby in time are also likely to be close in value5Q1696Q2927Q314511) Use Data … Data Analysis … Moving Average ) to generate a 3 and 5 time period moving average chart8Q4107(See image below)9Q18610Q211111Q315712Q412213Q18814Q210915Q31 5916Q4131 Data Measured
- 7. Moving average period (3 or 5) Check to generate chart Moving Average2Time IndexQuarterSales1Q173ERROR:#N/AERROR:#N/A2Q290ERR OR:#N/AERROR:#N/A3Q312194.6666666667ERROR:#N/A4Q4 98103ERROR:#N/A5Q1699690.26Q29286.3333333333947Q314 51021058Q4107114.6666666667102.29Q186112.666666666799. 810Q2111101.3333333333108.211Q3157118121.212Q41221301 16.613Q188122.3333333333112.812) Using visual inspection, discuss the differences between the 3 and 5 period Moving Averages charts14Q2109106.3333333333117.415Q3159118.66666666671 2716Q4131133121.8 3 Quarter Moving Average Actual 73 90 121 98 69 92 145 107 86 111 157 122 88 109 159 131 Forecast #N/A #N/A 94.666666666666671 103 96 86.333333333333329 102 114.66666666666667 112.66666666666667 101.33333333333333 118 130 122.33333333333333 106.33333333333333 118.66666666666667 133 Time Points Sales 5 Quarter Moving Average Actual 73 90 121 98 69 92 145 107 86 111 157 122 88 109 159 131 Forecast #N/A #N/A #N/A #N/A 90.2 94 105 102.2 99.8 108.2 121.2 116.6 112.8 117.4 127 121.8 Time Points Sales HW Week 7 (Submit in PDF format only) Time-series data is collected, on a subject, over a sequence of time periods. For this HW assignment , it is assumed the data are gathered over one particular interval of time (for instance: weekly, daily, monthly, yearly etc … and no varied combination of these particular intervals is considered)
- 8. The goal , when analyzing a time-series, is to produce predictions (forecast) of the measurement taken on the subject at some future time interval. There are many approaches to generating a forecast when conducting time-series analyses. However, in this HW assignment, you will explore some of the built in features available in Excel that can be used for time- series investigations. We’ll assume that past patterns that may be present in the time- series data that you are assigned continue into the future. For this week’s activity, you’ll use your assigned time-series dataset. Directions 1) Open the HW Dataset. Examine the first row and based on the first letter of your last name, identify the timeseries data you are to use when completing this assignment. 2) Review and Use the Time Series Excel Practice workbook, posted to Moodle, as your guide to investigate this time-series data. Apply all the steps as specified in the workbook and respond to each question or prompt. Submit and Format all tables and charts to class expectations to avoid formatting point loss. See Exemplars and class notes posted to Moodle. 3) Post your results to Moodle in PDF format. Your writeup should include each prompt presented in the Time-series Excel Practice workbook, the number of the prompt, your responses to the prompts, and all generated charts and tables. Charts and tables are expected to be formatted to class expectations (see Exemplar). DO NOT SUBMIT the EXCEL time series data set Sheet1First Letter of Your Last NameA-MN- ZDATEDJIADATENASDAQ9-Feb8270.879-Feb1591.569- Jan8000.869-Jan1476.428-Dec8776.398-Dec1577.038- Nov8829.048-Nov1535.578-Oct9336.938-Oct1720.958- Sep10850.668-Sep2091.888-Aug11543.558-Aug2367.528- Jul11378.028-Jul2325.558-Jun11350.018-Jun2292.988- May12638.328-May2522.668-Apr12820.138-Apr2412.808-