1. Create a time series object of 80 random normal observations with mean of 10, and standard deviation of 5. The time series object should be monthly starting in January 1950. Save this object as a variable named q1_ts and plot it.
a <- rnorm(80, mean = 10, sd = 5)
q1_ts <- ts(a, start = c(1950, 1), frequency = 12)  
plot(q1_ts)

  1. Using the q1_ts data from question 1, compute 3-period and 5-period, 2-sided moving averages on your dataset. Save them as variables x3_MA and x5_MA then plot the original series with both 3-period (blue) and 5-period (red) moving average lines. Include an appropriate title to your plot.
# not sure how to resolve this issue #
#a <- rnorm(80, mean = 10, sd = 5)
#q1_ts <- ts(a, start = c(1950, 1), frequency = 12)  
#plot(q1_ts)
#require(stats)
#require(ggplot2)
#require(ggfortify)
#x3_MA <- stats::filter(q1_ts, rep(1/3, 3), sides = 2)
#x5_MA <- stats::filter(q1_ts, rep(1/5, 5), sides = 2)
#x3x5 <- cbind(x3_MA, x5_MA)
#q2_plot <- autoplot(q1_ts) + lines(x3_MA, col = "blue") + lines(x5_MA, col = "red")
#title("Time Series Plot with Moving Averages")
  1. Using decomposition, explain whether you would use an additive or multiplicative model for the nottem dataset. Explain why and show any work.
data(nottem)  # Average Monthly Temperatures at Nottingham, 1920–1939
require(forecast)
## Loading required package: forecast
require(ggplot2)
## Loading required package: ggplot2
# look for underlying season or trend using moving average
ggseasonplot(nottem)

  # seasonal change clearly correlates with average monthly temp & it is clearly constant over time - b/c of this we will use additive decomposition
  1. Describe the difference between the covariance of a sample and the covariance of a population. Does the cov function in R compute a sample or population covariance?
# To calculate the covariance for sample data, we use a multiplier of (1/n-1). For population data, we use (1/N). The function cov() calculates sample covariance.
    1. Use the swiss data set. Calculate the correlation between Catholicism and Fertility. Calculate the correlation between Agriculture and Fertility. Describe what the two numbers tell you.
data(swiss)  # Swiss Fertility and Socioeconomic Indicators (1888) Data
require(stats)
c_f_corr <- cor(x= swiss$Catholic, y = swiss$Fertility, method = "pearson")
c_f_corr
## [1] 0.4636847
a_f_corr <- cor(x= swiss$Agriculture, y = swiss$Fertility, method = "pearson")
a_f_corr
## [1] 0.3530792
# Using the Pearson method to measure linear correlation, we see that Fertility is more strongly (positively) correlated with Catholicism (0.4636847) than with Agriculture (0.3530792).

rmarkdown::render(“~/Library/Mobile Documents/comappleCloudDocs/Term 4/Time Series”)