Time Series Analysis and Forecasting . Introduction. A time series is a set of observations generated sequentially in time Continuous vs. discrete time series
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
xt = Ft + xt
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Economic and business planning
Inventory and production control
Control and optimization of industrial processes
Lead time of the forecasts
is the period over which forecasts are needed
Degree of sophistication
Simple ideas
Moving averages
Simple regression techniques
Complex statistical concepts
BoxJenkins methodology
ForecastingTime Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Causeandeffect approach
Approaches to forecastingTime Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Advantages
Quickly and easily applied
A minimum of data is required
Reasonably shortto mediumterm forecasts
They provide a basis by which forecasts developed through other models can be measured against
Disadvantages
Not useful for forecasting into the far future
Do not take into account external factors
Causeandeffect approach
Advantages
Bring more information
More accurate mediumto longterm forecasts
Disadvantages
Forecasts of the explanatory time series are required
Approaches to forecasting (cont.)Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
(B) = 0 + 1B + 2B2 + …..
BmXt = Xt  m
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Better control
Improved design
Methods for estimating transfer function models
Classical methods
Based on deterministic perturbations
Uncontrollable disturbances (“noise”) are not accounted for, and hence, these methods have not always been successful
Statistical methods
Make allowance for “noise”
The BoxJenkins methodology
Transfer function modeling (cont.)Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Feedback control
Deviation from target output
P
P
N
N
t
t
Deviation from
target output

+
1
f
1


+
d
w
1
b
1
f
1
L
(
B
)
L
(
B
)
B
(
B
)
(
B
)
B
L
(
B
)
L
(
B
)
B
1
2
1
2
Compensating
Compen
sating
variable X
variable X
t+
t+
Control equation
Control equation
z
t
Process controlTime Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Model identification
Model estimation
Is model adequate ?
No
Modify model
Yes
Forecasts
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
(1st order) xt = (1 – B)xt = xt – xt1
(2nd order) 2xt = (1 – B)2xt = xt – 2xt1 + xt2
“B” is the backward shift operator
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
How can we determine the number of regular differencing ?
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
(
B
)
White noise
x
t
Linear filter
e
t
The linear filter modelTime Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
If the current observation xt depends on past observations with weights which decrease as we go back in time, the series is called invertible
For a linear process to be invertible,
Stationarity and invertibility conditions for a linear filterTime Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Stationarity and invertibility conditions
Theoretical ACs and PACs
Model identificationTime Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
For a linear process to be invertible,
Stationarity and invertibility conditionsTime Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
i.e., the roots of the characteristic equation 1  a1B = 0 lie outside the unit circle
k = a1k k > 0
i.e., for a stationary AR(1) model, the theoretical autocorrelation function decays exponentially to zero, however, the theoretical partialautocorrelation function has a cut off after the 1st lag
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
b
ì
=
ï
1
k
1
r
=
+
b
2
í
1
k
1
ï
>
0
k
1
î
Invertibility requirements for a MA(1) modeli.e., the roots of the characteristic equation 1  b1B = 0 lie outside the unit circle
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray
Time Series Analysis Lecture Notes MA(4030)Prepared By TMJA Cooray