Lecture 15 Chapter 8: Time series analysis and forecasting | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

CHAPTER 8: TIME SERIES ANALYSIS AND FORECASTING 8.1. Time series patterns 8.2. Forecast accuracy 8.3. Trend projection 8.4. Time series decomposition. Each of the independent variables zj (where j = 1, 2, . . . , p) is a function of x1, x2, . . . , xk (the variables for which data are collected). In some cases, each zj may be a function of only one x variable. Tài liệu giúp bạn tham khảo, ôn tập và đạt kết quả cao. Mời bạn đọc đón xem!

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Môn: Applied statistics (ENEE1006IU)

Trường: Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

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Profile Nhi Nhi
lOMoARcPSD| 45903860
APPLIED STATISTICS
COURSE CODE: ENEE1006IU
Lecture 15:
Chapter 8: Time series analysis and
forecasng
(3 credits: 2 is for lecture, 1 is for lab-work)
1
lOMoARcPSD| 45903860
2
CHAPTER 8: TIME SERIES ANALYSIS AND FORECASTING
•8.1. Time series paerns
•8.2. Forecast accuracy
•8.3. Trend projecon
•8.4. Time series decomposion
lOMoARcPSD| 45903860
LINEAR MODEL
Each of the independent variables z
j
(where j = 1, 2, . . . , p) is a funcon of x
1
, x
2
, . . . , x
k
(the variables for which data
are collected).
In some cases, each z
j
may be a funcon of only one x variable.
straight-line relaonship
simple rst-order model with one predictor variable
curvilinear relaonship
interacon
second-order model with two predictor variable
second-order model with one predictor variable
lOMoARcPSD| 45903860
4
lOMoARcPSD| 45903860
LINEAR REGRESSION ESTIMATION PROCESS
Simple regression
lOMoARcPSD| 45903860
6
LINEAR REGRESSION ESTIMATION PROCESS
Mulple regression
lOMoARcPSD| 45903860
8.3. TREND PROJECTION
•Linear Trend Regression: A me series technique that computes a forecast with
trend by drawing a straight line through a set of data using
lOMoARcPSD| 45903860
8
8.3. TREND PROJECTION
lOMoARcPSD| 45903860
8.3. TREND PROJECTION
•Nonlinear Trend Regression: a curvilinear funcon appears to be needed to model
the long-term trend:
Quadrac trend equaon:
Exponenal trend equaon:
lOMoARcPSD| 45903860
10
lOMoARcPSD| 45903860
DECOMPOSITION OF THE TOTAL DEVIATION IN A LINEAR
i
i
i
i
i
i
i
i
i
lOMoARcPSD| 45903860
12
CORRELATION COEFFICIENT - HOW GOOD IS THE FIT?
•Correlaon coecient (r) measures the direcon and strength of the linear
relaonship between two variables.
The closer the r value is to 1.0 the beer the regression line ts the data points.
•Coecient of determinaon (r
2
) measures the amount of variaon in the
dependent variable about its mean that is explained by the regression line.
provides a measure of the goodness of t for the esmated regression equaon
•Values of (r
2
) close to 1.0 are desirable.
lOMoARcPSD| 45903860
HOW GOOD IS THE REGRESSION
lOMoARcPSD| 45903860
14
RESIDUAL ANALYSIS
i
i
lOMoARcPSD| 45903860
DETECTING OUTLIERS AND INFLUENTIAL OBSERVATIONS
•Outliers: The presence of one or more outliers in a data set tends to increase s,
the standard error of the esmate increase , , the standard deviaon of
residual i
•Inuenal observaons: the value of the independent variable may have a strong
inuence on the regression results
lOMoARcPSD| 45903860
16
THE F TEST OF A MULTIPLE REGRESSION MODEL
lOMoARcPSD| 45903860
DECOMPOSITION OF THE SUM OF SQUARES AND THE ADJUSTED
COEFFICIENT OF DETERMINATION
lOMoARcPSD| 45903860
18
MEASURES OF PERFORMANCE IN MULTIPLE REGRESSION AND THE ANOVA
TABLE
lOMoARcPSD| 45903860
8.4. TIME SERIES DECOMPOSITION
•Time series decomposion can be used to separate or decompose a me series
into seasonal, trend, and irregular components.
get a beer understanding of the me series
an addive model is appropriate in situaons where the seasonal uctuaons do
not depend upon the level of the me series.
lOMoARcPSD| 45903860
20
8.4. TIME SERIES DECOMPOSITION
•If the seasonal uctuaons change over me, growing larger as the sales volume
increases because of a long-term linear trend, then a mulplicave model should
be used
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lOMoAR cPSD| 45903860 APPLIED STATISTICS COURSE CODE: ENEE1006IU Lecture 15:
Chapter 8: Time series analysis and forecasting
(3 credits: 2 is for lecture, 1 is for lab-work) 1 lOMoAR cPSD| 45903860
CHAPTER 8: TIME SERIES ANALYSIS AND FORECASTING •8.1. Time series patterns •8.2. Forecast accuracy •8.3. Trend projection
•8.4. Time series decomposition 2 lOMoAR cPSD| 45903860 LINEAR MODEL
Each of the independent variables zj (where j = 1, 2, . . . , p) is a function of x1, x2, . . . , xk (the variables for which data are collected).
In some cases, each zj may be a function of only one x variable. straight-line relationship
simple first-order model with one predictor variable curvilinear relationship
second-order model with one predictor variable interaction
second-order model with two predictor variable lOMoAR cPSD| 45903860 4 lOMoAR cPSD| 45903860
LINEAR REGRESSION ESTIMATION PROCESS Simple regression lOMoAR cPSD| 45903860
LINEAR REGRESSION ESTIMATION PROCESS Multiple regression 6 lOMoAR cPSD| 45903860 8.3. TREND PROJECTION
•Linear Trend Regression: A time series technique that computes a forecast with
trend by drawing a straight line through a set of data using lOMoAR cPSD| 45903860 8.3. TREND PROJECTION 8 lOMoAR cPSD| 45903860 8.3. TREND PROJECTION
•Nonlinear Trend Regression: a curvilinear function appears to be needed to model the long-term trend: Quadratic trend equation: Exponential trend equation: lOMoAR cPSD| 45903860 10 lOMoAR cPSD| 45903860 i i i i i i i i i
DECOMPOSITION OF THE TOTAL DEVIATION IN A LINEAR lOMoAR cPSD| 45903860
CORRELATION COEFFICIENT - HOW GOOD IS THE FIT?
•Correlation coefficient (r) measures the direction and strength of the linear
relationship between two variables.
The closer the r value is to 1.0 the better the regression line fits the data points.
•Coefficient of determination (r2) measures the amount of variation in the
dependent variable about its mean that is explained by the regression line.
provides a measure of the goodness of fit for the estimated regression equation
•Values of (r2) close to 1.0 are desirable. 12 lOMoAR cPSD| 45903860 HOW GOOD IS THE REGRESSION lOMoAR cPSD| 45903860 RESIDUAL ANALYSIS i i 14 lOMoAR cPSD| 45903860
DETECTING OUTLIERS AND INFLUENTIAL OBSERVATIONS
•Outliers: The presence of one or more outliers in a data set tends to increase s,
the standard error of the estimate increase , , the standard deviation of residual i
•Influential observations: the value of the independent variable may have a strong
influence on the regression results lOMoAR cPSD| 45903860
THE F TEST OF A MULTIPLE REGRESSION MODEL 16 lOMoAR cPSD| 45903860
DECOMPOSITION OF THE SUM OF SQUARES AND THE ADJUSTED COEFFICIENT OF DETERMINATION lOMoAR cPSD| 45903860
MEASURES OF PERFORMANCE IN MULTIPLE REGRESSION AND THE ANOVA TABLE 18 lOMoAR cPSD| 45903860
8.4. TIME SERIES DECOMPOSITION
•Time series decomposition can be used to separate or decompose a time series
into seasonal, trend, and irregular components.
get a better understanding of the time series
an additive model is appropriate in situations where the seasonal fluctuations do
not depend upon the level of the time series. lOMoAR cPSD| 45903860
8.4. TIME SERIES DECOMPOSITION
•If the seasonal fluctuations change over time, growing larger as the sales volume
increases because of a long-term linear trend, then a multiplicative model should be used 20