1-Define the following terms: a-Constant and Increasing seasonal variation b-Fir
ID: 3182999 • Letter: 1
Question
1-Define the following terms:
a-Constant and Increasing seasonal variation
b-First-Order Autocorrelation
c-State three types of trends
2-he following MINITAB output is for a set of time series
Predictor Coef SE Coef T P
Constant 5.28662 0.01694 75.97 0.00
t 0.004874 0.00154 31.53 0.000
t2 0.002700 0.00542 29.97 0.001
Q1 -0.00322 0.02090 -2.07 0.012
Q2 -0.04373 0.02089 -6.88 0.000
Q3 -0.05298 0.02088 -4.45 0.000
S = 0.0316709 R-Sq = 98.7% R-Sq(adj) = 96.7%
Analysis of Variance
Source DF SS MS F P
Regression 05 6.92205 0.57684 132.19 0.000
Residual Error 42 0.14413 0.00174
Total 47 7.06618
Durbin-Watson statistic = 1.87587
Use the above output to:
a-Write the general forecasting equation and thus predict the values of the coming four months.
b-Test the first-order autocorrelation
c-If the error terms are autocorrelation with 1 = 0.3129, construct a 95% PI for Y49
3-For a certain growth model based on 48 observations the prediction equation is given by:
lnY = 2.118+ 0.1225 t
a-Use the regression equation to estimate the following three period .
c-Estimate the growth rate of the data.
c-Use the growth rate to forecast Y49 given that Y48 = 2900, compare the result with (a).
Explanation / Answer
a)The following two structures are considered for basic decomposition models:
1. Additive: xt = Trend + Seasonal + Random
2. Multiplicative: xt = Trend * Seasonal * Random
The “Random” term is often called “Irregular” in software for decompositions.
The additive model is useful when the seasonal variation is relatively constant over time.The multiplicative model is useful when the seasonal variation increases over time.
b)
Autocorrelation can take on two types: positive or negative. In positive autocorrelation, consecutive errors usually have the same sign: positive residuals are almost always followed by positive residuals, while negative residuals are almost always followed by negative residuals. In negative autocorrelation, consecutive errors typically have opposite signs: positive residuals are almost always followed by negative residuals and vice versa.
In addition, there are different orders of autocorrelation. The simplest, most common kind of autocorrelation,first-order autocorrelation, occurs when the consecutive errors are correlated. Second-order autocorrelationoccurs when error terms two periods apart are correlated, and so forth.
c) There are three types of trend: Uptrends,Downtrends and Sideways/Horizontal Trends (The latter occurs when there is minimal movement up or down in the peaks and troughs). Some chartists consider that a sideways trend is actually not a trend on its own, but a lack of a well-defined trend in either direction.
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