"Dr. N.S. Gandhi Prasad" wrote:

> Hello
>
>     I am presently working on a project to study the relation between
> incidence of pest attacks such as aphids, Jassids, Bollworms etc and weather
> parameters. Earlier attempts could not lead to any meaningful conclusions.
>
>     I have 15 years weekwise data on weather parameters such as Max Temp,
> Min Temp, Rel. Humidity ( Morning & Evening ) Rainfall, Sunshine hours and
> percent of incidence of pest attack
>
>     I request the members to suggest some appropriate Statistical Tools.
>
>     Thanks in advance
>
>     ( Dr. N. S. Gandhi Prasad )
>
>     mail me
>     [log in to unmask]

Whereas all statisticians know regression , when time series data is used more
comprehensive techniques are required. They fall unser the class of Transfer
Function Models.One has to be aware of both erros of omission and errors of
comission. Bartlett warned about spurious correlation between time series.
Spurious correlation can be detected and dealt with with time-series methods
while the effect of interventions which often cause simple tools to not find
relationships can be identified and incorporated into the model.


Following is a brief introduction to time series analysis

Time series = a sequence of observations taken on a variable or multiple
variables at successive points in time.

Objectives of time series analysis:

1. To understand the structure of the time series (how it depends on time,
itself, and other time series variables)

2. To forecast/predict future values of the time series

What is wrong with using regression for modeling time series?

* Perhaps nothing. The test is whether the residuals satisfy the regression
assumptions: linearity, homoscedasticity, independence, and (if necessary)
normality. It is important to test for Pulses or one-time unusual values and to
either adjust the data or to incorporate a Pulse Intervention variable to
account for the identified anomaly.

Unusual values can often arise Seasonally , thus one has to identify and
incorporate Seasonal Intervention variables.

Unusual values can often arise at successive points in time earmarking the need
for either a Level Shift Intervention to deal with the proven mean
shift in the residuals.

* Often, time series analyzed by regression suffer from autocorrelated
residuals. In practice, positive autocorrelation seems to occur much more
frequently than negative.

* Positively autocorrelated residuals make regression tests more significant
than they should be and confidence intervals too narrow; negatively
autocorrelated residuals do the reverse.

* In some time series regression models, autocorrelation makes biased estimates,
where the bias cannot be fixed no matter how many data points or
observations that you have.

To use regression methods on time series data, first plot the data over time.
Study the plot for evidence of trend and seasonality. Use numerical tests
for autocorrelation, if not apparent from the plot.

* Trend can be dealt with by using functions of time as predictors. Sometimes we
have multiple trends and the trick is to identify the beginning and
end periods for each of the trends.

* Seasonality can be dealt with by using seasonal indicators (Seasonal Pulses)
as predictors or by allowing specic auto-dependence or auto-projection
such that the historical values ( Y(t-s) ) are used to predict Y(t)

* Autocorrelation can be dealt with by using lags of the response variable Y as
predictors.

* Run the regression and diagnose how well the regression assumptions are met.

* the residuals should have approximately the same variance (homoscedasticity)
otherwise some form of "weighted" analysis might be needed.

* the model form/parameters should be invariant i.e. unchanging over time. If
not then we perhaps have too much data and need to determine at what
points in time the model form or parameters changed.

                                                   Problems and Opportunities

* 1. How to determine the temporal relationship for each input series ,i.e. is
the relationship contemporaneous, lead or lag or some combination ? (
How to identify the form of a multi-input transfer function without assuming
independence of the inputs .)

* 2. How to determine the arima model for the noise structure reflecting omitted
variables.

* 3. How to do this in a ROBUST MANNER where pulses, seasonal pulses , level
shifts and local time trends are identified and incorporated.

* 4. How to test for and include specific structure to deal with non-constant
variance of the error process.

* 5. How to test for and treat non-constancy of parameters or model form.

Time series data presents a number of problems/opportunities that standard
statistical packages either avoid or ignore whereas we focus on them. AUTOBOX
implements the ideas suggested herein.

Hope this helps


DAVID P. REILLY   Automatic Forecasting Systems Inc.
Box 563, Hatboro Pa, 19040, USA  215-675-0652
<A HREF="mailto:[log in to unmask]">[log in to unmask]</A>
<A HREF="http://www.autobox.com">HOME PAGE FOR AUTOBOX</A>

P.S. Queens University in Belfast has used AUTOBOX to study animal diseases as
it relates to weather,rainfall etc. . Please contact me for the particulars,
perhaps by phone.



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