Lecture 15 - ENEE1006IU

 

Tài liệu học tập môn Applied statistics (ENEE1006IU) tại Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh. Tài liệu gồm 26 trang giúp bạn ôn tập hiệu quả và đạt điểm 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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lOMoARcPSD|364906 32
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)
Instructor: TRAN THANH TU Email:
tttu@hcmiu.edu.vn
tttu@hcmiu.edu.vn 1
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 2
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
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 3
LINEAR MODEL
Each of the independent variables z
j
(where j = 1, 2, . . . , p) is a function of x
1
, x
2
, . . . , x
k
(the variables for which data
are collected).
In some cases, each z
j
may be a function of only one x variable.
straight-line relationship
simple first-order model with one predictor variable
curvilinear relationship
interaction
second-order model with two predictor variable
second-order model with one predictor variable
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 4
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 5
LINEAR REGRESSION ESTIMATION PROCESS
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 6
Simple regression
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 7
LINEAR REGRESSION ESTIMATION PROCESS
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 8
Multiple regression
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 9
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
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 10
8.3. TREND PROJECTION
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 11
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 12
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:
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 13
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 14
DECOMPOSITION OF THE TOTAL DEVIATION IN A LINEAR
i
i
i
i
i
i
i
i
i
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 15
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 (r
2
) 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
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 16
•Values of (r
2
) close to 1.0 are desirable.
HOW GOOD IS THE REGRESSION
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 17
RESIDUAL ANALYSIS
i
i
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 18
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
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 19
THE F TEST OF A MULTIPLE REGRESSION MODEL
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 20
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 21
DECOMPOSITION OF THE SUM OF SQUARES AND THE ADJUSTED
COEFFICIENT OF DETERMINATION
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 22
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 23
MEASURES OF PERFORMANCE IN MULTIPLE REGRESSION AND THE ANOVA
TABLE
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 24
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 25
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.
lOMoARcPSD|364906 32
tttu@hcmiu.edu.vn 26
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
| 1/26
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lOMoARcPSD|364 906 32 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)
Instructor: TRAN THANH TU Email: tttu@hcmiu.edu.vn tttu@hcmiu.edu.vn 1 lOMoARcPSD|364 906 32
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 tttu@hcmiu.edu.vn 2 lOMoARcPSD|364 906 32 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 tttu@hcmiu.edu.vn 3 lOMoARcPSD|364 906 32 tttu@hcmiu.edu.vn 4 lOMoARcPSD|364 906 32
LINEAR REGRESSION ESTIMATION PROCESS tttu@hcmiu.edu.vn 5 lOMoARcPSD|364 906 32 Simple regression tttu@hcmiu.edu.vn 6 lOMoARcPSD|364 906 32
LINEAR REGRESSION ESTIMATION PROCESS tttu@hcmiu.edu.vn 7 lOMoARcPSD|364 906 32 Multiple regression tttu@hcmiu.edu.vn 8 lOMoARcPSD|364 906 32 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 tttu@hcmiu.edu.vn 9 lOMoARcPSD|364 906 32 8.3. TREND PROJECTION tttu@hcmiu.edu.vn 10 lOMoARcPSD|364 906 32 tttu@hcmiu.edu.vn 11 lOMoARcPSD|364 906 32 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: tttu@hcmiu.edu.vn 12 lOMoARcPSD|364 906 32 tttu@hcmiu.edu.vn 13 lOMoARcPSD|364 906 32 i i i i i i i i i tttu@hcmiu.edu.vn 14
DECOMPOSITION OF THE TOTAL DEVIATION IN A LINEAR lOMoARcPSD|364 906 32
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 tttu@hcmiu.edu.vn 15 lOMoARcPSD|364 906 32
•Values of (r2) close to 1.0 are desirable. HOW GOOD IS THE REGRESSION tttu@hcmiu.edu.vn 16 lOMoARcPSD|364 906 32 RESIDUAL ANALYSIS i i tttu@hcmiu.edu.vn 17 lOMoARcPSD|364 906 32
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 tttu@hcmiu.edu.vn 18 lOMoARcPSD|364 906 32
THE F TEST OF A MULTIPLE REGRESSION MODEL tttu@hcmiu.edu.vn 19 lOMoARcPSD|364 906 32 tttu@hcmiu.edu.vn 20 lOMoARcPSD|364 906 32
DECOMPOSITION OF THE SUM OF SQUARES AND THE ADJUSTED COEFFICIENT OF DETERMINATION tttu@hcmiu.edu.vn 21 lOMoARcPSD|364 906 32 tttu@hcmiu.edu.vn 22 lOMoARcPSD|364 906 32
MEASURES OF PERFORMANCE IN MULTIPLE REGRESSION AND THE ANOVA TABLE tttu@hcmiu.edu.vn 23 lOMoARcPSD|364 906 32 tttu@hcmiu.edu.vn 24 lOMoARcPSD|364 906 32
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. tttu@hcmiu.edu.vn 25 lOMoARcPSD|364 906 32
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 tttu@hcmiu.edu.vn 26
Document Outline

  • APPLIED STATISTICS
    • CHAPTER 8: TIME SERIES ANALYSIS AND FORECASTING
    • LINEAR MODEL
    • LINEAR REGRESSION ESTIMATION PROCESS
    • LINEAR REGRESSION ESTIMATION PROCESS (1)
      • 8.3. TREND PROJECTION
      • 8.3. TREND PROJECTION (1)
      • 8.3. TREND PROJECTION (2)
        • DECOMPOSITION OF THE TOTAL DEVIATION IN A LINEAR
        • HOW GOOD IS THE REGRESSION
        • DETECTING OUTLIERS AND INFLUENTIAL OBSERVATIONS
        • THE F TEST OF A MULTIPLE REGRESSION MODEL
          • DECOMPOSITION OF THE SUM OF SQUARES AND THE ADJUSTED COEFFICIENT OF DETERMINATION
          • MEASURES OF PERFORMANCE IN MULTIPLE REGRESSION AND THE ANOVA TABLE
      • 8.4. TIME SERIES DECOMPOSITION
      • 8.4. TIME SERIES DECOMPOSITION (1)