Jubilee Manual

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Package ‘jubilee’
September 1, 2018
Type Package
Title Forecast Long-Term Growth of the U.S. Stock Market
Version 0.2.3
Date 2018-09-01
Author Stephen H-T. Lihn [aut, cre]
Maintainer Stephen H-T. Lihn 
Description
A long-term forecast model called ``Jubilee-Tectonic model'' is implemented to forecast future returns of the U.S. stock market, Treasury yield, and gold price. The five-factor model can forecast the 10-year and 20-year future equity returns with high R-squared above 80 percent. It is based on linear growth and mean reversion characteristics in the U.S. stock market. In addition, this model enhances the CAPE model of Robert Shiller by introducing the hypothesis that there are fault lines in the historical CAPE, which can be calibrated and corrected through statistical learning.
URL https://ssrn.com/abstract=3156574
Depends R (>= 3.3.0)
Imports stats, yaml, utils, xts, zoo, splines, parallel, graphics,
methods, readxl, data.table, lmtest
Suggests knitr, R.rsp, testthat, roxygen2, scales, shape
VignetteBuilder R.rsp
License Artistic-2.0
Encoding UTF-8
LazyData true
RoxygenNote 6.1.0
Collate 'daily2fraction-method.R' 'fraction2daily-method.R'
'jubilee-adj-fault-line-method.R' 'jubilee-calc-cape-method.R'
'jubilee-package.R' 'jubilee-class.R' 'jubilee-constructor.R'
'jubilee-eqty-ols-method.R' 'jubilee-forward-rtn-method.R'
'jubilee-fred-data-method.R' 'jubilee-locate-file.R'
'jubilee-mcsapply-method.R' 'jubilee-ols-method.R'
'jubilee-predict-method.R' 'jubilee-read-fred-file.R'
'jubilee-repo-class.R' 'jubilee-repo-config.R'
'jubilee-repo-constructor.R' 'jubilee-std-fault-line-method.R'
'tri-wave-class.R' 'tri-wave-constructor.R' 'tri-wave-model.R'
NeedsCompilation no
1

2

jubilee-package

R topics documented:
jubilee-package . . .
daily2fraction . . . .
fraction2daily . . . .
jubilee . . . . . . . .
jubilee-class . . . . .
jubilee.adj_fault_line
jubilee.calc_cape . .
jubilee.eqty_ols . . .
jubilee.forward_rtn .
jubilee.fred_data . .
jubilee.locate_file . .
jubilee.mcsapply . .
jubilee.ols . . . . . .
jubilee.predict . . . .
jubilee.read_fred_file
jubilee.repo . . . . .
jubilee.repo-class . .
jubilee.repo.config .
jubilee.std_fault_line
tri.wave . . . . . . .
tri.wave class . . . .
triangle . . . . . . .

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Index

jubilee-package

2
3
3
4
5
5
6
7
7
8
9
9
10
11
12
13
13
14
14
15
16
16
18

jubilee: A package to forecast long-term growth of the US stock market.

Description
The jubilee package provides the core class and functions to forecast long-term growth of the U.S.
stock market. A tutorial is provided to demonstrate how to use this package and explain the relation
between the mathematical notations and the functions and data columns in this package.
Author(s)
Stephen H-T. Lihn
References
Stephen H.T. Lihn, "Jubilee Tectonic Model: Forecasting Long-Term Growth and Mean Reversion in the U.S. Stock Market." Available at SSRN: https://ssrn.com/abstract=3156574 or DOI:
http://dx.doi.org/10.2139/ssrn.3156574

3

daily2fraction

Converter from daily Date to fraction

daily2fraction

Description
Utility to convert from daily Date (R’s Date object) to fraction.
Usage
daily2fraction(d)
Arguments
array of Date object, or string in ISO yyyy-mm-dd format

d
Value

numeric, year in fraction convention
Author(s)
Stephen H. Lihn
Examples
daily2fraction(as.Date("2017-01-15")) # 2017.038
daily2fraction(as.Date("2017-02-14")) # 2017.122
daily2fraction(as.Date("2017-07-15")) # 2017.538

Converter from fraction to daily Date

fraction2daily

Description
Utility to convert from fraction to daily Date (R’s Date object).
Usage
fraction2daily(fraction)
Arguments
fraction

numeric, representing year in fraction convention.

Value
array of Date object
Author(s)
Stephen H. Lihn

4

jubilee

Examples
fraction2daily(2017.038) # 2017-01-15
fraction2daily(2017.125) # 2017-02-15

jubilee

Constructor of the jubilee class

Description
Construct an jubilee object which holds raw and derived data, channel regression results, and other
derived analytical quantities. This object is the main object to perform various forecasts and analyses.
Usage
jubilee(dtb, lookback.channel = 45, fwd.rtn.duration = 20)
Arguments
dtb

data.table from the jubilee.repo object, typically it is the ie slot. The user is
allowed to provide custom data object to research different markets, as long as
the column names are compliant.

lookback.channel
numeric, look-back channel in years to calculate mean-reversion. Default is 45.
fwd.rtn.duration
numeric, forward return duration in years. Default is 20.
Value
an object of the jubilee class
Author(s)
Stephen H. Lihn
Examples
## Not run:
repo <- jubilee.repo(online=FALSE)
ju <- jubilee(repo@ie, 45, 20)
## End(Not run)

5

jubilee-class

The jubilee class

jubilee-class

Description
This S4 class stores raw and derived data, channel regression settings and results.
Slots
call the match.call slot.
lookback.channel numeric, the look-back channel in years.
fwd.rtn.duration numeric, the forward return duration in years.
reg.dtb data.table, contains the regression data.
dtb data.table, contains the consolidated market data.
rate.spread.mean numeric, the mean of the yield spread, used to calculate rate.spread.norm
column.
create.time POSIXct, records the creation time of this object.

jubilee.adj_fault_line
Adjust the time series by fault lines

Description
This utility is used to adjust the time series by the provided fault lines.
Usage
jubilee.adj_fault_line(fraction, ts, fl, months = 1)
Arguments
fraction

numeric, representing year in fraction convention.

ts

numeric, time series to be adjusted, typically it is log.cape10 or log.cape20.

fl

the fault line matrix. See jubilee.std_fault_line() for more detail. If it is
provided as character string, it will be looked up as the name of data set in the
standard fault line library. If it is provided as numeric array, it will be converted
to a matrix.

months

interval in months to ramp up the fault line. Default is 1.

Value
numeric, ts adjusted by fault lines
Author(s)
Stephen H. Lihn

6

jubilee.calc_cape

Examples
## Not run:
repo <- jubilee.repo(online=FALSE)
dj <- jubilee(repo@ie, 45, 10)@reg.dtb
dj$log.cape10.adj <- jubilee.adj_fault_line(dj$fraction, dj$log.cape10, "r_nom_f10_5ftr_4fl")
## End(Not run)

jubilee.calc_cape

Internal utility to calculate n-year CAPE

Description
This CAPE calculator replicates the methodology of Shiller, so that one can calculate n-year CAPE,
e.g. n=20. This utility has been calibrated by original 10-year CAPE data from Shiller.
Usage
jubilee.calc_cape(dtb, period, tol.frac = 1/6)
Arguments
dtb

data.table

period

numeric, the backward-looking regression period

tol.frac

numeric, tolerance of missing data in the beginning of the time series, expressed
as fraction. Default is 1/6, that is, two months.

Value
numeric, the same length as dtb$fraction.
Author(s)
Stephen H. Lihn
Examples
## Not run:
dtb <- jubilee.repo(online=FALSE)@ie
cape10 <- jubilee.calc_cape(dtb, 10)
cape20 <- jubilee.calc_cape(dtb, 20)
## End(Not run)

7

jubilee.eqty_ols

Internal utility to calculate OLS regression for log total return index

jubilee.eqty_ols

Description
Calculate the OLS regression for log total return index
Usage
jubilee.eqty_ols(dtb, end.frac, lookback.channel, tol.frac = 1/6)
Arguments
dtb

data.table that contains fraction and log.tri columns.

end.frac
numeric, the ending fraction of regression.
lookback.channel
numeric, the backward-looking regression period
tol.frac

numeric, tolerance of missing data in the beginning, expressed as fraction. Default is 1/6, that is, two months.

Value
two-element array c(a,R) if end.frac is length-one; data.table with end.frac as fraction column
if end.frac is an array.
Author(s)
Stephen H. Lihn
Examples
## Not run:
dtb <- jubilee.repo(online=FALSE)@ie
jubilee.eqty_ols(dtb, 1970, 50) # c(11.8671626, 0.1008371)
## End(Not run)

jubilee.forward_rtn

Internal utility to calculate annualized forward and backward return

Description
Calculate the annualized forward and backward return on the given time series. The forward return
is typically the response variable in a forecast. The backward return is often used as explanatory
variable in a regression.
Usage
jubilee.forward_rtn(fraction, ts, fwd.rtn.duration, tol.frac = 1/12)
jubilee.backward_rtn(fraction, ts, bwd.rtn.duration, tol.frac = 1/12)

8

jubilee.fred_data

Arguments
fraction

numeric, the ending fraction of regression

ts
numeric, the time series data
fwd.rtn.duration
numeric, the forward-looking regression period
numeric, tolerance of missing data in the beginning, expressed as fraction. Default is 1/12, that is, one month.
bwd.rtn.duration
numeric, the backward-looking regression period
tol.frac

Value
numeric, the same length as fraction
Author(s)
Stephen H. Lihn
Examples
## Not run:
dtb <- jubilee.repo(online=FALSE)@ie
dtb$fwd.rtn.10 <- jubilee.forward_rtn(dtb$fraction, dtb$log.tri, 10)
dtb$bwd.rtn.10 <- jubilee.backward_rtn(dtb$fraction, dtb$log.tri, 10)
head(subset(dtb, fraction >= 1990),1)$fwd.rtn.10 # 1/1990+10y: 0.16745
tail(subset(dtb, fraction <= 2000+1/12),1)$bwd.rtn.10 # the same as above
## End(Not run)

jubilee.fred_data

Internal utility to download time series data from FRED

Description
This utility downloads time series from FRED. Many time series that this package uses are available
on FRED. Therefore, this utility is used to provide daily or monthly updates by concatenating live
data to the internal static data.
Usage
jubilee.fred_data(symbol, col_out = "Close")
Arguments
symbol

character, the name of the time series

col_out

character, the name of the output closing price column. Default is "Close"

Value
The xts object for the time series

9

jubilee.locate_file
Examples
## Not run:
jubilee.fred_data("VIXCLS") # VIX
## End(Not run)

jubilee.locate_file

Internal utility to locate static file

Description
This utility returns the path to internal file
Usage
jubilee.locate_file(local_file, stop = TRUE)
Arguments
local_file

character, the file name of an internal file.

stop

logical, whether to stop if file can’t be located. Default is TRUE.

Value
The path to the file, or else, an empty string
Author(s)
Stephen H. Lihn
Examples
jubilee.locate_file("UNRATE.csv")

jubilee.mcsapply

Wrapper to calculate sapply using multi-core

Description
This utility calculates sapply using multi-core capability. It is a simple wrapper on simplify2array
and parallel::mclapply. It is particularly convenient on Linux and Mac when parallelism saves
significant amount of computing time.
Usage
jubilee.mcsapply(x, FUN, ...)

10

jubilee.ols

Arguments
x

numeric

FUN

the function to be applied to each element of x

...

optional arguments to FUN

Value
numeric
Author(s)
Stephen H. Lihn
Examples
a <- seq(1,100)
jubilee.mcsapply(a, function(x) x^2) # use multi-core!

jubilee.ols

Internal utility to calculate OLS regression

Description
Calculate the OLS regression for a given time series and fraction
Usage
jubilee.ols(fraction, ts, lookback.channel, tol.frac = 1/6)
Arguments
fraction

numeric, the ending fraction of regression

ts
numeric, the time series data
lookback.channel
numeric, the backward-looking regression period
tol.frac

numeric, tolerance of missing data in the beginning, expressed as fraction. Default is 1/6, that is, two months.

Value
data.table with columns of fraction, lm.a, lm.y, lm.r
Author(s)
Stephen H. Lihn
References
See Section 2.3 of Stephen H.T. Lihn, "Jubilee Tectonic Model: Forecasting Long-Term Growth and
Mean Reversion in the U.S. Stock Market." Available at SSRN: https://ssrn.com/abstract=3156574
or http://dx.doi.org/10.2139/ssrn.3156574

11

jubilee.predict
Examples
## Not run:
dtb <- jubilee.repo(online=FALSE)@ie
df <- jubilee.ols(dtb$fraction, dtb$log.tri, 50)
subset(df, fraction > 1970 & fraction < 1970.05)
# fraction
lm.a
lm.r
lm.y
# 1970.042 11.86401 0.1007617 0.02103105
## End(Not run)

jubilee.predict

Make prediction based on linear regression

Description
Make prediction based on the linear regression of the forward return. Refer to the tutorial for more
detail.
Usage
jubilee.predict(object, lm, data)
jubilee.predict_real(object, lm, data)
Arguments
object

object of jubilee class

lm

the linear model

data

data used to predict (similar to newdata of stats::predict)

Value
data.table containing the prediction
Author(s)
Stephen H. Lihn
References
See Section 7 of Stephen H.T. Lihn, "Jubilee Tectonic Model: Forecasting Long-Term Growth and
Mean Reversion in the U.S. Stock Market." Available at SSRN: https://ssrn.com/abstract=3156574
or http://dx.doi.org/10.2139/ssrn.3156574

12

jubilee.read_fred_file

jubilee.read_fred_file
Internal utility to read FRED file

Description
This utility reads the internal static file, optionally amends with FRED online data, and returns the
values of a given symbol.

Usage
jubilee.read_fred_file(fraction, local_file, symbol, online = FALSE,
daily_symbol = NULL)

Arguments
fraction

numeric, the fraction to return the value. The utility will lookup within a month
to find value. For debug purpose, set it to NULL, and the intermediate data table
will be returned.

local_file

character, the file name of an internal file. For debug purpose, set it to NULL,
and the process will initiate the source data from FRED via symbol, instead of
a local file.

symbol

character, the FRED symbol.

online

logical, whether to fetch online data from FRED. Default is FALSE.

daily_symbol

character, the FRED symbol to read daily data that supplements the monthly
data. Default is NULL.

Value
The values of the symbol, numeric with the same length as fraction.

Author(s)
Stephen H. Lihn

Examples
repo <- jubilee.repo(online=FALSE)
a <- jubilee.read_fred_file(repo@ie$fraction, "BAA.csv", "BAA")
tail(a)

13

jubilee.repo

Constructor of jubilee.repo class

jubilee.repo

Description
Construct a jubilee.repo class by combining data from that of Robert Shiller since 1871, historical stock market data from 1802 to 1987 by William Schwert, 3-month Treasury bill rate, gold
price, and several other economic time series from FRED. Optionally, this function can fetch more
recent data from the website of Robert Shiller and Federal Reserve FRED website if the R session
has connection to the internet.
Usage
jubilee.repo(online = TRUE)
Arguments
online

logical, indicating whether to fetch data from online resource or not. Default is
TRUE.

Value
An object of jubilee.repo class
Author(s)
Stephen H. Lihn
Examples
repo <- jubilee.repo(online=FALSE)
dtb <- repo@ie
tail(dtb,1)

jubilee.repo-class

The jubilee repository class

Description
This S4 class stores the raw data for the jubilee package
Slots
call The match.call slot
ie data.table, contains the combined data from ie.raw, ws, and inflation.
yield.inversion numeric, the fractions of yield curve inversion
raw.ie data.table, contains the data from ie_data.xls of Robert Shiller
ws data.table, contains the historical market return data from William Schwert

14

jubilee.std_fault_line
inflation data.table, contains the historical inflation data from Minneapolis FED
comm.int data.table, contains the historical commercial interest rate
tb3ms data.table, contains the historical 3-month Treasury bill rate
gold data.table, contains the historical monthly gold prices
gold2 data.table, contains the historical annual gold prices
create.time POSIXct, records the creation time of this object.

jubilee.repo.config

Configuration of jubilee’s data repository

Description
This utility stores the data configuration for the jubilee’s data repository. This is used internally
to provide proper abstraction to the data sources, such as file name, URL, FRED symbol, column
name, decimal format, etc.
Usage
jubilee.repo.config()
Value
The list of data elements and their attributes.
Author(s)
Stephen H. Lihn
Examples
c <- jubilee.repo.config()
c$ie$url

jubilee.std_fault_line
Standard fault line data sets

Description
This method defines a collection of standard fault line data sets that have been analyzed and optimized in the research. It is intended for end users to produce standard regressions, forecasts, and
charts quickly.
Usage
jubilee.std_fault_line(name)

15

tri.wave
Arguments
name

character, the name of the collection. If "list" is supplied, the list of names will
be returned. If a numeric array is supplied, it will be converted to a matrix
format.

Value
numeric, pairs of fault lines, each is c(year, delta)
Author(s)
Stephen H. Lihn
Examples
jubilee.std_fault_line("r_nom_f10_5ftr_4fl")
jubilee.std_fault_line("r_nom_f20_5ftr_2fl")
jubilee.std_fault_line("r_nom_f20_5ftr_2fl_ramp5y")

tri.wave

Constructor of tri.wave class

Description
Construct an tri.wave object to simulate the triangular wave model.
Usage
tri.wave()
Value
an object of tri.wave class
Author(s)
Stephen H. Lihn
Examples
w <- tri.wave()

16

triangle

tri.wave class

The triangular wave model class

Description
This S4 class defines the parameters in the triangular wave model.
Slots
call the match.call slot.
a.t numeric, the look-back channel in years
a0 numeric, the look-back channel in years
s1 numeric, the forward return duration in years
s2 numeric, the start fraction of in-sample training period
y.mean numeric, the end fraction of in-sample training period
y.amp numeric, the end fraction of in-sample training period
y.t numeric, the end fraction of in-sample training period
y.p numeric, the end fraction of in-sample training period
References
See Section 4 of Stephen H.T. Lihn, "Jubilee Tectonic Model: Forecasting Long-Term Growth and
Mean Reversion in the U.S. Stock Market." Available at SSRN: https://ssrn.com/abstract=3156574
or http://dx.doi.org/10.2139/ssrn.3156574

triangle

Methods of triangular wave model

Description
Methods of triangular wave model
Usage
triangle(t, p)
tri.wave.s(object, t)
tri.wave.a(object, t)
tri.wave.y(object, t)
tri.wave.x(object, t)
tri.wave.logr.y(object, t, p)
tri.wave.logr(object, t, p)

17

triangle

tri.wave.logr.semi(object, t)
tri.wave.logr.quarter(object, t)
Arguments
t

the time vector in fraction

p

the period of the triangle wave

object

the object of tri.wave class

Value
numeric
Author(s)
Stephen H. Lihn
References
See Section 4 of Stephen H.T. Lihn, "Jubilee Tectonic Model: Forecasting Long-Term Growth and
Mean Reversion in the U.S. Stock Market." Available at SSRN: https://ssrn.com/abstract=3156574
or http://dx.doi.org/10.2139/ssrn.3156574
Examples
w <- tri.wave()
t <- seq(1900, 2000, by=1)
tri.wave.y(w, t)

Index
∗Topic class
jubilee-class, 5
jubilee.repo-class, 13
tri.wave class, 16
∗Topic constructor
jubilee, 4
jubilee.repo, 13
tri.wave, 15
∗Topic data
jubilee.fred_data, 8
jubilee.locate_file, 9
jubilee.read_fred_file, 12
jubilee.repo.config, 14
∗Topic model
jubilee.adj_fault_line, 5
jubilee.predict, 11
jubilee.std_fault_line, 14
triangle, 16
∗Topic utility
daily2fraction, 3
fraction2daily, 3
jubilee.calc_cape, 6
jubilee.eqty_ols, 7
jubilee.forward_rtn, 7
jubilee.mcsapply, 9
jubilee.ols, 10

jubilee.predict, 11
jubilee.predict_real (jubilee.predict),
11
jubilee.read_fred_file, 12
jubilee.repo, 13
jubilee.repo-class, 13
jubilee.repo.config, 14
jubilee.std_fault_line, 14
tri.wave, 15
tri.wave class, 16
tri.wave.a (triangle), 16
tri.wave.logr (triangle), 16
tri.wave.s (triangle), 16
tri.wave.x (triangle), 16
tri.wave.y (triangle), 16
triangle, 16

daily2fraction, 3
fraction2daily, 3
jubilee, 4
jubilee-class, 5
jubilee-package, 2
jubilee.adj_fault_line, 5
jubilee.backward_rtn
(jubilee.forward_rtn), 7
jubilee.calc_cape, 6
jubilee.eqty_ols, 7
jubilee.forward_rtn, 7
jubilee.fred_data, 8
jubilee.locate_file, 9
jubilee.mcsapply, 9
jubilee.ols, 10
18
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