TianyuDu/AnnEconForecast

---
title: "Set_13_LSTAR"
output: html_notebook
---

Set data directory path
```{r setup, include=FALSE, cache = FALSE}
library(knitr)
opts_knit$set(root.dir = "C:/Teaching/Undergrad/data ECO374")
```

Install and load required packages
```{r}
if (!require("tsDyn")) install.packages("tsDyn")
library(tsDyn)
library(xts)
library(anytime)
```

Download data on U.S. Industrial Production, Quarterly, Continuously Compounded Rate of Change
Remove any lines with missing values
Source: https://fred.stlouisfed.org/series/INDPRO
Load, convert to xts format, and plot
```{r}
setwd("C:/Teaching/Undergrad/data ECO374")
data_IP_full <- read.csv(file="INDPRO.csv", header=TRUE, sep=",")
xtsdata_IP <- xts(x=data_IP_full[c("INDPRO_CCH")], order.by=anytime(data_IP_full$DATE))
plot.xts(xtsdata_IP, plot.type = c("single"), main ="U.S. Industrial Production, Q rate of change" , legend.loc = "topleft", grid.col="lightgray")
```

Estimate an LSTAR model
```{r}
LSTAR <- lstar(xtsdata_IP$INDPRO_CCH, m=1, d=1, mL=1, mH=1, gamma=1, th=1)
summary(LSTAR)
```

Obtain a linear model approximation
```{r}
maxlag <- 24
ACF <- acf(as.vector(xtsdata_IP$INDPRO_CCH), lag.max=maxlag, plot = FALSE)
PACF <- pacf(as.vector(xtsdata_IP$INDPRO_CCH), lag.max=maxlag, plot = FALSE)
par(mfcol=c(1,2), mai=c(0.4, 0.4, 0.7, 0.1), cex.main=0.9)
plot(ACF[1:maxlag], main="ACF")
plot(PACF[1:maxlag], main="PACF")
```

Compare model fit (AIC) with LSTAR
```{r}
mlin <- arima(xtsdata_IP$INDPRO_CCH, order = c(1,0,0), include.mean=TRUE)
summary(mlin)
```