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Objectives




6.1 Seasonal autoregressive moving average (SARMA) models



6.1.1 Question: Which of [S2] and/or [S3] is a SARMA model?




6.1.2 Question: Why do we assume a multiplicative structure in [S1]?

  • What theoretical and practical advantages (or disadvantages) arise from requiring that an ARMA model for seasonal behavior has polynomials that can be factored as a product of a monthly polynomial and an annual polynomial?




6.1.3 Fitting a SARMA model

  • Let’s do this for the full, monthly, version of the Lake Huron data described in Section 5.5.

  • First, we’ll revisit reading in the data.

system("head huron_depth.csv",intern=TRUE)
##  [1] "# downloaded on 1/24/16 from\r"                                                    
##  [2] "# http://www.glerl.noaa.gov/data/dashboard/data/levels/mGauge/miHuronMog.csv\r"    
##  [3] "# Lake Michigan-Huron:, Monthly Average Master Gauge Water Levels (1860-Present)\r"
##  [4] "# Source:, NOAA/NOS\r"                                                             
##  [5] "Date, Average\r"                                                                   
##  [6] "01/01/1860,177.285\r"                                                              
##  [7] "02/01/1860,177.339\r"                                                              
##  [8] "03/01/1860,177.349\r"                                                              
##  [9] "04/01/1860,177.388\r"                                                              
## [10] "05/01/1860,177.425\r"
dat <- read.table(file="huron_depth.csv",sep=",",header=TRUE)
dat$Date <- strptime(dat$Date,"%m/%d/%Y")
dat$year <- as.numeric(format(dat$Date, format="%Y"))
dat$month <- as.numeric(format(dat$Date, format="%m"))
head(dat)
##         Date Average year month
## 1 1860-01-01 177.285 1860     1
## 2 1860-02-01 177.339 1860     2
## 3 1860-03-01 177.349 1860     3
## 4 1860-04-01 177.388 1860     4
## 5 1860-05-01 177.425 1860     5
## 6 1860-06-01 177.461 1860     6
huron_depth <- dat$Average
time <- dat$year + dat$month/12 # Note: we treat December 2011 as time 2012.0, etc
plot(huron_depth~time,type="l")