LINREG

linreg(options) depvar start end residuals

# list

where: depvar The dependent variable.

start end The range to use in the regression. The default is the largest common range of all variables in the regression.

residuals Series name for the residuals. Omit if you do not want to save the regression residuals.

list The list of explanatory variables.

Examples of LIN

lin y# constant x

lin y 1991:12 2001:8 # constant x

lin y 1991:12 2001:8 resids# constant y{1 2 5}

lin y / resids# constant y{1 to 4}

Internal Variables

LINREG creates a number of variables that you can use in subsequent computations. A partial list of these variables is:

 

%BETA The coefficient vector. The first coefficient estimated is %BETA(1), the second %BETA(2), and so on. For example, in the output for dlja above, the constant is %BETA(1), the coefficient for dlja{1} is %BETA(2), and so forth.

%tstats The vector of t-stats

%NDF Degrees of freedom.

%NOBS Number of observations.

%NREG Number of regressors.

%RSS Residual sum of squares.

%RSQUARED Centered R2 (i.e, the usual measure of R2)

%SEESQ Standard error of estimate squared

Correlate

Correlate(options) series start end (saveseries)where: series The series used to compute the correlations.Results= series used to save the correlations NUMBER= The number of autocorrelations to compute. The default is the integer value of one-fourth the total number of observations. PARTIAL= Series for the partial autocorrelations. If you omit this option, the PACF will not be calculated.QSTATS Use this option if you want the Ljung-Box Q-statistics.SPAN= Use with qstats to set the width of the intervals tested. For example, with quarterly data, you can set span = 4, to obtain Q(4), Q(8), Q(12), and so forth.

The AIC and the SBC

com sbc = nobs*log(%rss) + %nreg*log(%nobs)

compute aic = %nobs*log(%rss) + 2*%nreg

display 'AIC' aic 'SBC' sbc

BOXJENK

BOXJENK depvar start end residuals

Options AR=number of autoregressive parameters [0] MA=number of moving average parameters [0] iters= number of iterations SAR=number of seasonal autoregressive parameters [0] SMA=number of seasonal moving average parameters [0] DIFFS=number of regular differencings [0] SDIFFS=number of seasonal differencings [0] CONSTANT/[NOCONSTANT]

Technical Issues

Constant in the equation box(constant, ar=||1,4||, ma = 2) y

Negative values of the aic and bic aic = T ln(%rss) + 2*%nobs

To use the aic and bic, the models must be estimated over the same sample period. box(constant, ar=||1,4||, ma = 2) dly 90:1 * box(constant, ar=1, ma = 2) dly 90:1 *

Technical Issues 2

Did not converge error messageThe program cannot find the solution for

the coefficients that minimizes the residual sum of squares.

increase iters iters=50

The model is too complex (too unnecessary many parameters)

Transforming the series

When to difference?

When to use the log?

Graph the transformed series

Check ACF of the transformed series

The ACF

Label the graph of the autocorrelationsAlter bjident.srcWrite in the essential detailsplot the correlations yourself

ACF of the residuals

Bjident

@BJIDENT series start end

Options

DIFF=maximum regular differencings[0]

SDIFFS=maximum seasonal differencings[0]

TRANS=[NONE]/LOG/ROOT Transformation to apply to data

[GRAPH]/NOGRAPH

SPAN=seasonal span

0 Re gular 0 Se as ona l

0 5 10 15 20-1. 00

-0. 75

-0. 50

-0. 25

0. 00

0. 25

0. 50

0. 75

1. 00

CO RRSPARTI ALS

Forecastforecast(print) number steps start # equation forecasts 

number The number of equations in the system. In univariate forecasting, number is necessarily equal to 1.

steps The number of forecasts to create.start The starting period of the forecasts.equation The name of the previously defined equation.forecastsThe name of the series in which you want to save the

forecasts. This field is optional.  Exampleboxjenk(define=eq1,ar=1,ma=1) y / residsforecast(print) 1 5 101# eq1

Forecast -- New FORECAST equations

# equation forecasts  

FROM=starting period of the forecast intervalTO=ending period of the forecast intervalSTEPS=number of forecast steps to compute

• FROM and TO set the starting and ending periods for the forecasts, or • FROM and STEPS to set the starting date and number of steps (periods)PRINT/[NOPRINT]

Seasonality in the Box-Jenkins framework

Seasonal AR coefficientsyt = a1yt-1+a12yt-12 + a13yt-13

yt = a1yt-1+a12yt-12 + a1a12yt-13

(1 - a1L)(1 – a12L12)yt

Seasonal MA Coefficients

Seasonal differencing: = yt – yt-12

Seasonality in the Box-Jenkins framework

Seasonal AR coefficients yt = a1yt-1+a12yt-12 + a13yt-13

yt = a1yt-1+a12yt-12 + a1a12yt-13

(1 - a1L)(1 – a12L12)yt

Seasonal MA Coefficients

Seasonal differencing: Dyt = yt – yt-1 versus D12yt = yt – yt-12

NOTE: You do not difference 12 times dif(sdiffs=1) y / sdy