Annualised growth rate: least squares trend line (GRLS#)
This calculates the annualised growth rate between two dates,start and end dates, using the least squares trend line. The least squares trend line is used to determine an underlying growth rate instead of an actual growth rate. This is particularly useful when the start and end dates are eratic. A parameter N can be used to return N/A if there are any missing values in the data sample.
Formats
GRLS#(Expression,Start Date,End Date)
Actual dates are typed using either the standard DD/MM/YY format. or the displacement date formats, for example -NY.
As a date parameter one can also use YRE, HFE, QTE, MTE, WKE, LYE, BDATE, BDATEXXF
GRLS#(Expression)
If you do not specify start and end dates, the defaults are the start and end dates for the display period.
GRLS#(Expression,Period)
The rolling growth time period is entered next to the series.
GRLS #(Expression ,Period, Parameter )
The parameter set to N means that if there are any missing values in the data sample the output will be N/A.
Examples
GRLS#(ICI,1/1/93,1/1/94)
This calculates the annualised growth rate in the ICI share price between 1/1/93 and 1/1/94.
GRLS#(ICI)
This default format calculates the annualised growth rate in ICI share price between the start and end dates for the display period.
GRLS#(TOTMKUK(RI),10Y)
This format calculates the ten year annualised rolling growth rate of the total return of the Equity market.
GRLS#(CACPCOREF,3Y,N)
This calculates a rolling 3Y annualized growth rate for an Economics data series having some missing values. Output is N/A when there is data missing in the data set.
Formula for function
GRLS# calculates the annualised compound growth for as defined below. The calculated value is written throughout each year between the start and end dates. The calculation used is:
The least squares trend line b is calculated
b = Cxy/Cxx
Where:
and
N = number of values between start and end dates at the input frequency
Sy = ln(v0)+ ln(v1)+ ln(v2)+......ln(vN-1)
Sx = 0 + 1 + 2 + ... + (N-2) + (N-1)
Sx2 = 02 + 12 + 22 + ... + (N-2)2 + (N-1)2
Sxy = ln(v0)*0+ ln(v1)*1+ ln(v2)*2+......ln(vN-1)*N-1
vN = the value at date N
ln is the natural log
To then calculate the annualised compound growth -
100 * (exp (b * Na)-1)
Where
Na = is the average number of observations per year - 261 for daily frequency, 52 for weekly frequency, etc.