Time Series - correlation between two time series

[CJ Wilson]

Hello, I'm reading the book "Introduction to Time Series Using Stata" (by Sean Becketti) and had a question relating to the section below. The author is calculating the correlation between the change unemployment rate and the change in nonfarm payroll employment from Jan 1950 to Jan 2012. I'd like to adopt this approach on my own time series data, but am not exactly sure of their approach. When it says "change in the unemployment rate" and "change in nonfarm payroll employment" -> how is that calculated? For example, does one calculate the first order difference? (difference between each time point and the time point before?) Thank you for any thoughts!

[Ali Gokhan Yucel]

Yes, it refers to the first difference in time series analysis, which involves calculating the change in a variable between two consecutive time periods.

By downloading the monthly data for "All Employees: Total Nonfarm," also known as Total Nonfarm Payroll (measured in thousands of persons, seasonally adjusted), and the monthly unemployment rate (percent, seasonally adjusted) from FRED (Federal Reserve Economic Data), you can replicate the graph.

Below is a brief section of the data and the graph using the full dataset.

clear
input long PAYEMS double UNRATE
43526 6.5
43297 6.4
43954 6.3
44382 5.8
44718 5.5
45083 5.4
45454 5.0
46192 4.5
46438 4.4
46706 4.2
46776 4.2
46861 4.3
47288 3.7
47577 3.4
47873 3.4
47861 3.1
47952 3.0
48064 3.2
48061 3.1
48012 3.1
47954 3.3
48006 3.5
48147 3.5
48314 3.1
48296 3.2
48522 3.1
48504 2.9
48620 2.9
48642 3.0
48282 3.0
48143 3.2
48924 3.4
49320 3.1
49597 3.0
49816 2.8
50166 2.7
50144 2.9
50339 2.6
50473 2.6
50435 2.7
50490 2.5
50519 2.5
50536 2.6
50489 2.7
50368 2.9
50240 3.1
49908 3.5
49703 4.5
49469 4.9
49382 5.2
49157 5.7
49179 5.9
48965 5.9
48895 5.6
48835 5.8
48826 6.0
48886 6.1
48942 5.7
49180 5.3
49331 5.0
49496 4.9
49644 4.7
49962 4.6
50248 4.7
50512 4.3
50790 4.2
50987 4.0
51111 4.2
51266 4.1
51429 4.3
51592 4.2
51805 4.2
51975 4.0
52167 3.9
52294 4.2
52375 4.0
52506 4.3
52586 4.3
51955 4.4
52631 4.1
52604 3.9
52777 3.9
52821 4.3
52929 4.2
52887 4.2
53097 3.9
53156 3.7
53238 3.9
53150 4.1
53067 4.3
53123 4.2
53128 4.1
52934 4.4
52763 4.5
52558 5.1
52384 5.2
52076 5.8
51576 6.4
51299 6.7
51027 7.4
end

g date=_n

tsset date

g change_payems=d.PAYEMS

g change_unrate=d.UNRATE

scatter change_unrate change_payems, yline(0) xline(0) ytitle("Change in unemployment rate") xtitle("Change in nonfarm payroll(1000s)")

[CJ Wilson]

This is so helpful, thank you!!