R中财务数据的ARIMA模型选择

Question

我正在尝试根据财务数据拟合 arima 模型，但出现错误：

arima 中的错误(spReturnsOffset, order = c(p, d, q)) : non-stationary 来自 CSS 的 AR 部分

以下代码：

library(quantmod)


getSymbols("^GSPC", from="1950-01-01")
spReturns = diff(log(Cl(GSPC)))
#differenced logarithmic returns of the "Closing Price" of the S&P500 and strip out the initial NA value:
spReturns[as.character(head(index(Cl(GSPC)),1))] = 0

# Create the forecasts vector to store the predictions
windowLength = 500
foreLength = length(spReturns) - windowLength
forecasts <- vector(mode="character", length=foreLength)

for (f in 0:foreLength) {
    # Obtain the S&P500 rolling window for this day
    spReturnsOffset<- spReturns[(1+f):(windowLength+f)]


order.matrix <- matrix(0, nrow = 3, ncol = 4 * 4)
aic.vec <- numeric(4 * 4)
k <- 1
for (p in 1:4) for (q in 1:4) {
  order.matrix[, k] <- c(p,0,q)
  aic.vec[k] <- AIC(arima(spReturnsOffset, order=c(p, 0, q)))
  k <- k+1
  }
ind <- order(aic.vec, decreasing = FALSE)
aic.vec <- aic.vec[ind]
order.matrix <- order.matrix[, ind]
rownames(order.matrix) <- c("p", "d", "q")
order.matrix <- t(order.matrix)
result <- cbind(order.matrix, aic.vec)
colnames(result) <- c("p", "d", "q", "AIC")
}

我也在 arima 函数中尝试过 MLE 方法，但仍然收到错误消息：

solve.default(res$hessian * n.used, A) 中的错误：Lapack 例程 dgesv：系统完全是奇异的：U[1,1] = 0

我也尝试过使用 trycatch！代码一直在运行！

我该如何解决这个问题？

回应 Hack-R 的评论

以下代码确实有效：

# Obtain the S&P500 returns and truncate the NA value
getSymbols("^GSPC", from="1950-01-01")
spReturns = diff(log(Cl(GSPC)))
spReturns[as.character(head(index(Cl(GSPC)),1))] = 0

# Create the forecasts vector to store the predictions
windowLength = 500
foreLength = length(spReturns) - windowLength
forecasts <- vector(mode="character", length=foreLength)

for (d in 0:foreLength) {
    # Obtain the S&P500 rolling window for this day
    spReturnsOffset = spReturns[(1+d):(windowLength+d)]

    # Fit the ARIMA model
    final.aic <- Inf
    final.order <- c(0,0,0)
    for (p in 0:5) for (q in 0:5) {
        if ( p == 0 && q == 0) {
            next
        }

        arimaFit = tryCatch( arima(spReturnsOffset, order=c(p, 0, q)),
                             error=function( err ) FALSE,
                             warning=function( err ) FALSE )

        if( !is.logical( arimaFit ) ) {
            current.aic <- AIC(arimaFit)
            if (current.aic < final.aic) {
                final.aic <- current.aic
                final.order <- c(p, 0, q)
                final.arima <- arima(spReturnsOffset, order=final.order)
            }
        } else {
            next
        }
    }

Answer 1

以下代码符合我的要求，感谢您的阅读和建议。

#Get S&P 500
getSymbols("^GSPC", from = "2000-01-01")

#Compute the daily returns 
gspcRet<-diff(log(Cl(GSPC)))

#Use only the last two years of returns 
gspcTail<-as.ts(tail(gspcRet,500))

#Searching for the best models
order.matrix<-matrix(0,nrow = 3, ncol = 6 * 6)
aic.vec<- numeric(6 * 6)
k<-1
for(p in 0:5) for(q in 0:5){
    order.matrix[,k]<-c(p,0,q)
    aic.vec[k]<- AIC(arima(gspcTail, order=c(p,0,q)))
    k<-k+1
}
ind<- order(aic.vec,decreasing=F)
aic.vec<- aic.vec[ind]
order.matrix<- order.matrix[,ind]
order.matrix<- t(order.matrix)
result<- cbind(order.matrix,aic.vec)
colnames(result)<- c("p","d","q","AIC")