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Apr 3, 2024

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Department of Supply Chain and Business Technology Management ID-40230060 BSTA 677 - MANAGERIAL FORECASTING Quiz 1 - March 7, 2024 Instructions.  You have 120 minutes to submit your answers.  Use SAS code, SAS EG and/or Studio.  Your answers should be submitted as a Word document (LASTNAME.doc) with your results and supporting code pasted from SAS Studio/EG.  To submit zip your SAS EG/Studio project with the Word document.  Do not erase any questions. Write your answers below the questions.  Provide explanations to each question for full mark. Question 1. The purpose of the analysis is to examine quarterly US arrivals to Australia over time. The data is given in the SAS dataset USARV. Answers the following questions using SAS Studio, SAS EG or SAS code or their combinations. a) Construct a time plot of US arrivals. What features can you observe from the time plot? Explain. proc print data=tutorial.usarv; run; proc sort data=tutorial.usarv out=tutorial.usarv_sorted; by date; run; proc sgplot data=tutorial.usarv_sorted; title "Stock Prices"; series x=date y=Arrivals / lineattrs=(color=blue); xaxis grid; yaxis grid; run; Feature Observed -Increasing trend, seasonality, and variance can be seen as per below graph. 1

b) Apply an appropriate Moving Average (MA) filter to US arrivals. a. Choose and justify your MA window. What can you conclude? proc expand data=tutorial.usarv out=tutorial.usarv_MA; id Date; convert Arrivals = Arrivals_MA8 / method=none transout=(MOVAVE 8); proc sgplot data=tutorial.usarv_MA; series y=Arrivals x=Date / lineattrs=(color=gray) legendlabel="Arrivals"; series y=Arrivals_MA8 x=Date / lineattrs=(color=blue) legendlabel="Arrivals_MA8"; yaxis valueattrs=(color=black size=10pt); xaxis type=time valueattrs=(color=black size=10pt); Run; For a seasonal period, which is even and of order m, we use a 2×m-MA to estimate the trend-cycle. The data for USARV is quarterly data meaning m=4 therefore MA window will be 2*(4) which is 8MA. 2

Conclusion - With fewer severe highs and lows, the smoothed data is less erratic than the raw data. This facilitates the process of locating any hidden trends or patterns in the information. We can now discern a rising upward trend in the data from the smoothed data, and the seasonality impact has been reduced. b. Use MA of 3-year window and plot together with your original MA window. What’s the effect of increasing or decreasing length of MA window? Explain. proc expand data=tutorial.usarv out=tutorial.usarv_MA; id Date; convert Arrivals = Arrivals_MA8 / method=none transout=(MOVAVE 8); convert Arrivals = Arrivals_MA24 / method=none transout=(MOVAVE 24); proc sgplot data=tutorial.usarv_MA; series y=Arrivals x=Date / lineattrs=(color=gray) legendlabel="Arrivals"; series y=Arrivals_MA8 x=Date / lineattrs=(color=orange) legendlabel="Arrivals_MA8"; series y=Arrivals_MA24 x=Date / lineattrs=(color=blue) legendlabel="Arrivals_MA24"; yaxis valueattrs=(color=black size=10pt); xaxis type=time valueattrs=(color=black size=10pt); Run; 3

Expanding the window size of a Moving Average (MA) filter enhances the smoothness of time series data by diminishing its volatility, thereby facilitating the detection of underlying trends or patterns. This smoothing effect arises from averaging a greater number of data points, which inherently minimizes the influence of short- term variations and yields a more consistent signal. As the window size increases, it further averages out these fluctuations, leading to an even smoother outcome. Nonetheless, enlarging the MA window size is not without its challenges. A notable issue is the introduction of a lag in the signal, as the averaging process effectively shifts the smoothed signal ahead in time by an amount equivalent to the window size. Such a delay can be detrimental when the focus is on capturing immediate changes or variations in the data, which might be masked by the smoothing. Additionally, a larger MA window may also lead to a reduction in data detail and information. The process of smoothing tends to blur or eliminate minor fluctuations or noise within the data. If these minor variations hold crucial information, employing a large window size for smoothing could lead to significant information loss. Therefore, selecting the appropriate MA window size is a matter of balancing the analysis objectives with the data's inherent properties. Opting for a larger window size can be beneficial for unearthing long-term trends or patterns, whereas a smaller window size might be preferable for highlighting short-term variations. 4

c) Decompose US arrivals using multiplicative and additive approaches. How different they are? Which type of decomposition should you be using here and why? What are the distinct features of OK arrivals. /* Additive */ ods graphics on; proc timeseries data=tutorial.usarv outdecomp=tutorial.decomposed_data plots=(series decomp tc sc sa irregular); id date interval=qtr; var Arrivals; DECOMP tc sc sa IRREGULAR / MODE=additive; Run; /* Multiplicative */ ods graphics on; proc timeseries data=tutorial.usarv outdecomp=tutorial.decomposed_data plots=(series decomp tc sc sa irregular); id date interval=qtr; var Arrivals; DECOMP tc sc sa IRREGULAR / MODE=multiplicative; Run; 5

In additive decomposition, the model fails to account for variations in the amplitude of seasonal shifts, whereas multiplicative decomposition effectively captures these variations in seasonal data. Additionally, the additive approach may reveal some seasonality within the irregular components, which the multiplicative approach tends to eliminate. The multiplicative decomposition is deemed more fitting due to the observed variability in seasonal fluctuation magnitudes over time. Time Series Trend: This represents the time series' long-term direction or movement. The data exhibits a trend of gradual increase. Seasonality: This denotes predictable and systematic variations in the time series resulting from recurrent factors such as seasons, weekdays, or times of the day. Irregularity (Noise): This component consists of random, unpredictable fluctuations in the time series, not attributed to other components. These can arise from unforeseen events or measurement errors. Cyclicity: This refers to patterns or fluctuations that recur over lengths of time longer than those of seasonal patterns, without being tied to a specific season or time frame. Such cyclic behavior is not observed in this dataset. 6

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