library(tseries)library(forecast)library(fredr)fredr_set_key('25e01a7269f9d0fdd83a00ee95e51aee')HP=fredr( series_id = "NYSTHPI", observation_start = as.Date("1980-01-01"), observation_end = as.Date("2023-01-01"))head(HP)plot(HP$date,HP$value, type="l")HP_INY=ts(HP$value, frequency=4, start=c(1980,01))plot(HP_INY)head(HP_INY)trend=seq(HP_INY)trendtrend=1:173plot(trend)trendLinearModel_HPNY=tslm(HP_INY~trend)summary(LinearModel_HPNY)checkresiduals(LinearModel_HPNY)AIC(LinearModel_HPNY)BIC(LinearModel_HPNY)accuracy(LinearModel_HPNY)forecast_LinearModel_HPNY=forecast(LinearModel_HPNY, h=4)plot(forecast_LinearModel_HPNY)summary(forecast_LinearModel_HPNY)LinearModel_HPNY2=tslm(HP_INY~trend+season)checkresiduals(LinearModel_HPNY2) summary(LinearModel_HPNY2)AIC(LinearModel_HPNY2)BIC(LinearModel_HPNY2)accuracy(LinearModel_HPNY2)forecast_LinearModel_HPNY2=forecast(LinearModel_HPNY2, h=4)plot(forecast_LinearModel_HPNY2)summary(forecast_LinearModel_HPNY2)accuracy(forecast_LinearModel_HPNY2) gdp=fredr( series_id = "gdp", observation_start = as.Date("1980-01-01"), observation_end = as.Date("2023-01-01"))gdp=ts(gdp$value, frequency=4, start=c(1980,01))plot(gdp,HP_INY)LinearModel_HPNY3=tslm(HP_INY~trend+gdp)checkresiduals(LinearModel_HPNY3) # this is a wrongly specified model: mising an important variable or wrong functional form.head(gdp)summary(LinearModel_HPNY3)AIC(LinearModel_HPNY3)BIC(LinearModel_HPNY3)accuracy(LinearModel_HPNY3)predict(LinearModel_HPNY3, data.frame(trend=c(174,175,176), gdp=c(24000, 25000, 27000)), interval="confidence")plot(gdp,residuals(LinearModel_HPNY3))plot(fitted(LinearModel_HPNY3), residuals(LinearModel_HPNY3))

Please make areference to the video and the code | shared to complete this assignment. 1. Estimate the trend coefficient for House Price Index for the United States. The code from fred is USSTHPI. Please explain the estimated trend coefficient and if it is statistically significant. 2. Check the residuals and see if they are correlated. 3 Report AIC, BIC from the estimated model. 4. Forecast the next 4 quarters based on the trend. 5. Do the results change when you add the quadratic trend. Please explain. Report all the code and R results in aword document