What is lagged interest rate?

Question

I am trying to reproduce a plot in "Statistics and Data engineering for Financial Engineering" by D. Ruppert. The author uses the risk free returns data available in the Ecdat package in R. Specifically the rf variable in the Capm data set of this package. He wants to demonstrate that changes in the rate are more variable for large values of the rate (heteroskedacity). So in figure 4.19 (a) he plots the change in the rate vs the lagged rate, and indeed for larger values the points in the scatter plot are more dispersed. I want to reproduce this plot. But I have no idea what the "lagged rate" here means. Any ideas?

I have attached the plot below.

I would like to reconstruct figure 4.19 (a), but I'm not exactly sure what to plot on the x-axis.

Answer 1

Lagged means past values. The lag can be by as long as you want. If Interest Rates today are 0% and yesterday they were 0.25%. Yesterdays value is what we call the lagged value.

Let's say its now 2012 and we are looking at IR in yearly frequency. IR is 0.1%. To lag IR we simply look back at the last value. So what was IR last year? It was 0.3%. Notice how 0.3% is in IR(-1) for 2012 (which is the present). If the concept isn't clear just reread this more carefully. When your lagging a time series all your doing is making todays value, yesterday. How do you that, you shift the array down. Notice you can make the lag whaterver value you feel. IR(-2) means, your looking at IR 2 years ago. In the graph above, the author is simply trying to analyze the effect of yesterday's (past values of IR) on today's IR value. How much does the past values influence today's value? That's what the graphs are trying to delineate.

(Can someone help arrange the data matrix I wrote below, when its displayed it not formatted correctly. Thank you!)

Date IR IR(-1)<--Lagged Interest Rate 2008 1.5% -- 2009 1.1% 1.5% 2010 0.9% 1.1% 2011 0.3% 0.9% 2012 0.1% 0.3% 2013 -- 0.1%