使用R中的for循环将时间序列函数的值存储在数组中

Question

I am working with Bank of America time series data for stock prices. I am trying to store the forecasted value for a specific step ahead (in this case 1:20 steps) in an array. I then need to subtract each value of the array from each value of the test array. Then I have to square each value of the array, sum all the squared values of the array, then divide by N (N = number of steps forecasted ahead).

I have the following so far. Also, the quantmod and fpp libraries are needed for this.

---------Bank of America----------

library(quantmod)
library(fpp)

BAC = getSymbols('BAC',from='2009-01-02',to='2014-10-15',auto.assign=FALSE)
BAC.adj = BAC$BAC.Adjusted
BAC.daily=dailyReturn(BAC.adj,type='log')

test = tail(BAC.daily, n = 20)
train = head(BAC.daily, n = 1437)

Trying to write a function to forecast, extract requisite value (point forecast for time i), then store it in an array where I can perform operations on that array (ie - add, multiply, exponentiate, sum the values of the array)

MSE = function(N){
    for(i in 1:(N)){
        x = forecast(model1, h = i)
        y = x$mean
        w = as.matrix(as.double(as.matrix(unclass(y))))
        p = array(test[i,]-w[i,])
    }
}

and we also have:

model1 = Arima(train, order = c(0,2,0))
MSE = function(N){
    result = vector("list", length = (N))
    for(i in 1:(N)){
        x = forecast(model1, h = i)
        point_forecast = as.double(as.matrix(unclass(x$mean)))
        result[i] = point_forecast
    }
   result = as.matrix(do.call(cbind, result))
}

Neither of these functions have worked so far. When I run the MSE function, I get the following errors:

> MSE(20)
There were 19 warnings (use warnings() to see them)
> warnings()
Warning messages:
1: In result[i] = point_forecast :
number of items to replace is not a multiple of replacement length
2: In result[i] = point_forecast :
number of items to replace is not a multiple of replacement length
3: In result[i] = point_forecast :
number of items to replace is not a multiple of replacement length
4: In result[i] = point_forecast :

When I run MSE2 function, I get the following ouput:

MSE2(20) [1] -0.15824

When putting a print statement inside, it printed out 'p' as a singular number, just like above (even though that had been run for i = 20). The x,y, and w variable in the MSE2 function act as vectors as far as storing the output, so I do not understand why p does not as well.

I appreciate any help in this matter, thank you.

Sincerely,

Mitchell Healy

Answer 1

Your question has two MSE functions: one in the first code block and one in the second code block.

Also, library(forecast) is needed to run Arima and forecast .

My understanding of what you are trying to do in the first paragraph is to compute the 20-step ahead forecast error. That is, what is the error in forecasts from model1 20 days ahead, based on your test data. This can be done in the code below:

model1 <- Arima(train, order = c(0,2,0))
y_fcst<-forecast(model1,h=20)$mean
errors<-as.vector(y_fcst)-as.vector(test)
MSE.fcst<-mean(errors^2)

However, I'm not sure what you're trying to do here: an ARIMA(0,2,0) model is simply modelling the differences in returns as a random walk. That is, this model just differences the returns twice and assumes this twice-differenced data is white noise. There's no parameters other than $\\sigma^2$ being estimated.

Rob Hyndman has a blog post covering computing errors from rolling forecasts .

Answer 2

My solution to finding the MSE is below. I used log adjusted daily return data from Bank of America gathered through quantmod. Then I subsetted the data (which had length 1457) into training[1:1437] and testing[1438:1457].

The solution is:

forc = function(N){
   forecast = matrix(data = NA, nrow = (N) )
   for(i in 1:N){
      fit = Arima(BAC.adj[(1+(i-1)):(1437+(i-1))], order = c(0,0,4))
      x = forecast(fit, h = 1)
      forecast[i,] = as.numeric(x$mean)
   }
   error = test - forecast
   error_squared = error^2
   sum_error_squared = sum(error_squared)
   MSE = sum_error_squared/N
   MSE
}