tar: Estimation of a TAR model

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/tar.R

Description

Estimation of a two-regime TAR model.

Usage

1
2
3
tar(y, p1, p2, d, is.constant1 = TRUE, is.constant2 = TRUE, transform = "no",
 center = FALSE, standard = FALSE, estimate.thd = TRUE, threshold, 
method = c("MAIC", "CLS")[1], a = 0.05, b = 0.95, order.select = TRUE, print = FALSE)

Arguments

y

time series

p1

AR order of the lower regime

p2

AR order of the upper regime

d

delay parameter

is.constant1

if True, intercept included in the lower regime, otherwise the intercept is fixed at zero

is.constant2

similar to is.constant1 but for the upper regime

transform

available transformations: "no" (i.e. use raw data), "log", "log10" and "sqrt"

center

if set to be True, data are centered before analysis

standard

if set to be True, data are standardized before analysis

estimate.thd

if True, threshold parameter is estimated, otherwise it is fixed at the value supplied by threshold

threshold

known threshold value, only needed to be supplied if estimate.thd is set to be False.

method

"MAIC": estimate the TAR model by minimizing the AIC; "CLS": estimate the TAR model by the method of Conditional Least Squares.

a

lower percent; the threshold is searched over the interval defined by the a*100 percentile to the b*100 percentile of the time-series variable

b

upper percent

order.select

If method is "MAIC", setting order.select to True will enable the function to further select the AR order in each regime by minimizing AIC

print

if True, the estimated model will be printed

Details

The two-regime Threshold Autoregressive (TAR) model is given by the following formula:

Y_t = φ_{1,0}+φ_{1,1} Y_{t-1} +…+ φ_{1,p} Y_{t-p_1} +σ_1 e_t, \mbox{ if } Y_{t-d}≤ r

Y_t = φ_{2,0}+φ_{2,1} Y_{t-1} +…+φ_{2,p_2} Y_{t-p}+σ_2 e_t, \mbox{ if } Y_{t-d} > r.

where r is the threshold and d the delay.

Value

A list of class "TAR" which can be further processed by the by the predict and tsdiag functions.

Author(s)

Kung-Sik Chan

References

Tong, H. (1990) "Non-linear Time Series, a Dynamical System Approach," Clarendon Press Oxford

"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan

See Also

predict.TAR, tsdiag.TAR, tar.sim, tar.skeleton

Examples

1
2
data(prey.eq)
prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE)

Example output

Attaching package: 'TSA'

The following objects are masked from 'package:stats':

    acf, arima

The following object is masked from 'package:utils':

    tar

time series included in this analysis is:  log(prey.eq) 
SETAR(2, 1 , 4 ) model delay = 3 
estimated threshold =  4.661  from a Minimum AIC  fit with thresholds 
searched from the  17  percentile to the   81  percentile of all data.
The estimated threshold is the  56.6  percentile of
all data.
lower regime: 
Residual Standard Error=0.2341
R-Square=0.9978
F-statistic (df=2, 28)=6355.76
p-value=0

                       Estimate Std.Err t-value Pr(>|t|)
intercept-log(prey.eq)   0.2621  0.3156  0.8305   0.4133
lag1-log(prey.eq)        1.0175  0.0704 14.4455   0.0000




 (unbiased) RMS 
0.05479 
 with no of data falling in the regime being 
log(prey.eq) 30 


 (max. likelihood) RMS for each series (denominator=sample size in the regime) 
log(prey.eq) 0.05114 


 upper regime: 
Residual Standard Error=0.2676
R-Square=0.9971
F-statistic (df=5, 18)=1253.556
p-value=0

                       Estimate Std.Err t-value Pr(>|t|)
intercept-log(prey.eq)   4.1986  1.2841  3.2697   0.0043
lag1-log(prey.eq)        0.7081  0.2023  3.5005   0.0026
lag2-log(prey.eq)       -0.3009  0.3118 -0.9648   0.3474
lag3-log(prey.eq)        0.2788  0.4063  0.6861   0.5014
lag4-log(prey.eq)       -0.6113  0.2726 -2.2427   0.0377




 (unbiased) RMS 
0.07158 
 with no of data falling in the regime being 
23 


 (max. likelihood) RMS for each series (denominator=sample size in the regime)
0.05602 

 Nominal AIC is  10.92 

TSA documentation built on July 2, 2018, 1:04 a.m.