rollapply with Arima model: testing for stability of coefficients

N

nour88

New Member
#1
#1
Hi everyone,

I am trying to fit an arima model on a rolling window using rollapply.My aim is to plot a graph of the evolution of the coefficient, plot the error and the standard deviation.
well i encountered the following problems:

1) each window in the roll apply have different set of coeffcients: basically when i plot auto.arima()$coef[1] over time it could be ar1 or ma1 or anything.The reason i am doing this is that plotting the coefficient stability permits to judge the stability of coefficient and assess the accuracy of the model.

> getSymbols("ICICIBANK.NS");
> ICICIBANK.NS<-as.data.frame(ICICIBANK.NS)
> ICICIBANK.NS$returns<-c(NA,diff(log(ICICIBANK.NS$ICICIBANK.NS.Adjusted)))
> z<-ICICIBANK.NS$returns
> z<-na.omit(z)
> y<-rollapply(as.zoo(z),width=100,FUN=function(x) auto.arima(x)$coef[1])

basically i am trying here to have a look at the evolution of the first coefficient.but the model changes from one window to another.

Does anyone have an idea how solve this? or maybe some lead i can work on ?

2) when i do auto.arima to log returns i get an ARIMA(0,0,0) and when i dot it for raw raw prices i get ARIMA(3,1,3):
> getSymbols("ICICIBANK.NS");
[1] "ICICIBANK.NS"
> ICICIBANK.NS<-as.data.frame(ICICIBANK.NS)
> ICICIBANK.NS$returns<-c(NA,diff(log(ICICIBANK.NS$ICICIBANK.NS.Adjusted)))
> auto.arima(ICICIBANK.NS$returns)
Series: ICICIBANK.NS$returns
ARIMA(0,0,0) with zero mean

sigma^2 estimated as 0.003309: log likelihood=3042.76
AIC=-6083.51 AICc=-6083.51 BIC=-6077.86
> auto.arima(ICICIBANK.NS$ICICIBANK.NS.Adjusted)
Series: ICICIBANK.NS$ICICIBANK.NS.Adjusted
ARIMA(3,1,3) with drift

Coefficients:
ar1 ar2 ar3 ma1 ma2 ma3 drift
0.0741 -0.0998 0.5626 -0.0572 0.0662 -0.8633 0.1087
s.e. 0.0306 0.0323 0.0279 0.0192 0.0200 0.0159 0.0606

sigma^2 estimated as 77.62: log likelihood=-7610.48
AIC=15236.96 AICc=15237.02 BIC=15282.22

why would auto.arima() work with prices and not log returns ?
 
noetsi

noetsi

Fortran must die
#2
#2
If this is a software question, which I would guess, you probably want it in the pertinant software area not here. I am not sure what software you are using.
 
Dason

Dason

Ambassador to the humans
#3
#3
nour88 said:
basically i am trying here to have a look at the evolution of the first coefficient.but the model changes from one window to another.
Click to expand...
Then don't use auto.arima - just use arima to fit the same model every time.

nour88 said:
why would auto.arima() work with prices and not log returns ?
Click to expand...
Who said auto.arima isn't working? It gave you what it thought was the best model for the data under the constraints that you gave it. Sometimes that ends up being a very very simple model.

noetsi said:
If this is a software question, which I would guess, you probably want it in the pertinant software area not here. I am not sure what software you are using.
Click to expand...
You should be able to recognize at least some R by now ;)
 
noetsi

noetsi

Fortran must die
#4
#4
I guessed it was R dason :) but then there are lots of other software like say Matlab it could be and I was reluctant to mislead a poster :p

Well it's ok to mislead spunky...:p

There are many tools designed over the years to analyze ARIMA. I do not know how R uses them, but the OP might want to look at them and find out where R does them [or how I guess].
 
N

nour88

New Member
#6
#6
Thanks for your reply,

Well, basically what i am trying to find is if there is a model that is more appropriate on a window of N=50/100/200 days
over time.
I thought maybe by looking at the evolution of the models and coefficients we can come up with more robust model.

When i use all the data the model fitted by auto.arima() is far from the real data as you can see from plotted model versus real data.
I can see that after differencing the data is stationary but still the model ouput by auto arima is not conclusive.

library('tseries')
library(quantmod)
library(forecast)

ICICIBANK.NS <- getSymbols("ICICIBANK.NS", auto.assign=FALSE)[,6]
ICICIBANK.NSreturns <- diff(ICICIBANK.NS, log=TRUE, na.pad=FALSE)
big_ret <- which(abs(ICICIBANK.NSreturns)>.5) # finds erroneously large returns at start and end of period with bad data
bad_rows <- (big_ret[1]+1) : (big_ret[2])
bad_data <- ICICIBANK.NS[bad_rows]
ICICIBANK.NS <- ICICIBANK.NS[-bad_rows,]
ICICIBANK.NSreturns <- diff(ICICIBANK.NS, log=TRUE, na.pad=FALSE)

Box.test(ICICIBANK.NSreturns,lag=20,type="Ljung-Box")
adf.test(ICICIBANK.NSreturns,alternative="stationary")
acf(ICICIBANK.NSreturns)

ar_prices <- auto.arima(log(ICICIBANK.NS))
ar_returns <- auto.arima(ICICIBANK.NSreturns)

plot(ar_returns$x,col="red")
lines(fitted(ar_returns),col="blue")

mean_returns <- rollmean(ICICIBANK.NSreturns, k=100)
plot(mean_returns)

Is there any other model fitting technique than auto.arima that could produce more robust results? any leads?
 
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