ISYE 6402 Homework 4: Time Series Analysis of Domestic Passenger Counts Questions and Answers with complete

For this data analysis, you will analyze the daily and weekly domestic passenger count arriving in Hawaii airports. File DailyD contains the daily number of passengers between May 2019 and February 2023 File WeeklyD contains the weekly number of passengers for the same time period. Here we will use different ways of fitting the ARIMA model while dealing with trend and seasonality. library(lubridate) library(mgcv) library(tseries) library(car) Instructions on reading the data To read the data in R , save the file in your working directory (make sure you have changed the directory if different from the R working directory) and read the data using the R function () daily - ("DailyD", head = TRUE) daily$date - as.Date(daily$date) weekly - ("WeeklyD", head = TRUE) weekly$week - as.Date(weekly$week) Question 1. Trend and seasonality estimation 1a. Plot the daily and weekly domestic passenger count separately. Do you see a strong trend and seasonality? daily_ts = ts(daily$domestic,start=decimal_date(ymd("")),frequency=365) (daily_ts,ylab="Domestic Count") 1/21 2/ weekly_ts = ts(weekly$domestic,decimal_date(ymd("")),frequency=52) (weekly_ts,ylab="Domestic Count") Response: I see seasonality as well as a slight trend, as the peaks of the cycles are rising slightly overtime. It’s hard to tell exactly what the seasons are but it looks like there are typically two peaks within a year - one towards 2/21 2/ the beginning of the year and one a little after the middle of the year (maybe summer travel). 1b. (Trend and seasonality) Fit the weekly domestic passenger count with a non-parametric trend using splines and monthly seasonality using ANOVA. Is the seasonality significant? Plot the fitted values together with the original time series. Plot the residuals and the ACF of the residuals. Comment on how the model fits and on the appropriateness of the stationarity assumption of the residuals. 3/21 2/ ## Splines Trend Estimation = c(1:length(weekly_ts)) = c( - min())/max() #anova_monthly = season(weekly) month - r(month(weekly$week)) =gam(weekly_ts~s()+month) =ts(fitted(),start=decimal_date(ymd("")),frequency=52) resid_weekly_fit= ts((weekly_ts-fitted()),start=decimal_date(ymd("")),f requency=52) (resid_weekly_fit,ylab="Residual Process") 4/21 2/ acf(resid_weekly_fit) Response: The model seems to follow the time series data pretty well until the peaks get a little bigger in 2022. From the residual process, there seems to be increased variation as times goes on, which you can see when you compare the peaks at the beginning of 2020 and 2021 compared to the beginning of 2022 and end of 2022 The ACF plot of the residuals show no statistically significant pattern (because the lags diminish quickly), but we see some pattern that exhibits the seasonal periodicity. 1c. (Trend and seasonality) This time fit the daily domestic passenger count with a non-parametric trend using splines, monthly and day-of-the-week seasonality using ANOVA. Plot the fitted values together with the original time series. Are the seasonal effects significant? Plot the residuals and the ACF of the residuals. Comment on how the model fits and on the appropriateness of the stationarity assumption of the residuals. 5/21 2/ ## Splines Trend Estimation = c(1:length(daily_ts)) = c( - min())/max() #anova_monthly = season(weekly) month - r(month(daily$date)) =gam(daily_ts~s()+month) =ts(fitted(),start=decimal_date(ymd("")),frequency=365) resid_daily_fit= ts((daily_ts-fitted()),start=decimal_date(ymd("")),fre quency=365) (resid_daily_fit,ylab="Residual Process") 6/21 2/ acf(resid_daily_fit) Response: The residual process looks slightly better for the model on the daily time series as compared to the residual process for the model on the daily time series. However, we see in the ACF plot that although the lags diminish quickly, there still seems to be a cyclical pattern remaining.