• Credits

• Better understandings of the economic world

• And most importantly, your curiosities about the unknowns.

• Final exam (14 points): 50% on implementation, 50% on theory. Last year exam available on moodle. Quite easy.

• Two take-home exercises using R (3 points each): Empirical questions. To be published at the end of Oct and end of Nov.

• Slides available on moodle https://moodleucl.uclouvain.be/ under the name LECON2031

• Lectures: Theory and general ideas. Some discussions about implementations.

• Tutorials: user-oriented (how to solve take-home exercises).

• How do we (or I) see the economic world nowadays?

Problem 1. Projections may be misleading

Problem 2. Variables may be improperly measured

Problem 3. Their changes are caused by other hidden unmeasruable factors

Problem 4. Predictions are Alchemy type games.

If all these are untrustworthy, what do you believe? No answer to this question. (Perhaps yourself?)

• In order to better understand the game, we only investigate part of the game, the part that can be examined by ourselves…

• Namely, those measurable variables themselves, excluding the hidden unmeasurable factors.

Be interested in the values of the same variables with respect to time: Time series

What is time series?

• Time series: a sequence of observations over time.

• Time series is to describe the dynamical features.

• The growth of information over time.

• Do we solve the untrustworthy problem by looking at time series?

• No, the problem roots in the deeper layer (in the flow chart it should be the topmost layer).

• Other existing ways cannot tackle it either.

But time (and space) is the very few available element that can lift lower dimensional creatures (as human beings) to view their world with the angle from higher dimensions.

• The course will equip you with a device using time dimension.

• You may still get stuck in this low dimensional observable world.

• But at least, you will have an equipment for your further exploration.

• The curiosities persist our possibility of leaping into a higher dimension.

Reference:

• Introductory Time Series with R
• Time Series Analysis and Its Applications: With R Examples

Advanced Reference:

• Time Series Analysis: Forecasting and Control 5th Edition

• Using R for Introductory Statistics https://cran.r-project.org/doc/contrib/Verzani-SimpleR.pdf

• Install

R-Console https://www.r-project.org/

RStudio (IDE for R) http://www.rstudio.com Go to “Download RStudio Desktop”

x = rep(0,20)
x

##  [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

x[1] = 0; x[2] = 1
for(t in 3:20){x[t] = x[t-1] + x[t-2]}
x

##  [1]    0    1    1    2    3    5    8   13   21   34   55   89  144  233
## [15]  377  610  987 1597 2584 4181

plot(x)

• Current computer programming heavily depends on iterations.

• For example, the previous for loop iteration

for(t in 3:20){x[t] = x[t-1] + x[t-2]}

fulfills the Fibonacci sequence \[ x_t = x_{t-1} + x_{t-2}\] from \(x_1=0, x_2=1\) to \(x_{20} = 4181\). Here, time index is the number of iterations.

• Data information is stored as a matrix. In R, a vector can be numerical

a = c(90,60,50,55,20,40) 

• and can be characteristic

b = c("A","B","C","C","C","C")

• or even be logical (0=FALSE, 1=TRUE)

c = c(TRUE,TRUE,FALSE,FALSE,FALSE,FALSE) 
as.numeric(c)

## [1] 1 1 0 0 0 0

mydata = data.frame(a,b,c)
names(mydata) = c("Score","Level","Passed") 
mydata

##   Score Level Passed
## 1    90     A   TRUE
## 2    60     B   TRUE
## 3    50     C  FALSE
## 4    55     C  FALSE
## 5    20     C  FALSE
## 6    40     C  FALSE

mydata$Score

## [1] 90 60 50 55 20 40

as.matrix(mydata)

##      Score Level Passed 
## [1,] "90"  "A"   " TRUE"
## [2,] "60"  "B"   " TRUE"
## [3,] "50"  "C"   "FALSE"
## [4,] "55"  "C"   "FALSE"
## [5,] "20"  "C"   "FALSE"
## [6,] "40"  "C"   "FALSE"

matdata = as.matrix(mydata)
matdata[1,1]

## Score 
##  "90"

Several time series data repositories offer R APIs. For example:

• Quandl https://www.quandl.com/ (financial and economic data)

• WDI: World Development Indicators (World bank) https://data.worldbank.org/products/wdi (Country level data)

• Federal Reserve Bank of St.Louis https://fred.stlouisfed.org/

Let’s try to find some time series about the economy of Belgium. https://www.quandl.com/data/WWDI-World-Bank-World-Development-Indicators

library(Quandl)
BE_GDP = Quandl("WWDI/BEL_NY_GDP_PCAP_KN") 

tail(BE_GDP, n = 2)

FALSE          Date     Value
FALSE 57 1961-12-31 10422.791
FALSE 58 1960-12-31  9961.546

colnames(BE_GDP)=c("Time", "GDP per Capita")
tail(BE_GDP, n = 2)

FALSE          Time GDP per Capita
FALSE 57 1961-12-31      10422.791
FALSE 58 1960-12-31       9961.546

plot(BE_GDP)

BE_GDP_new = Quandl("WWDI/BEL_NY_GDP_PCAP_KN", type="xts") 
library(dygraphs); dygraphs::dygraph(BE_GDP_new, main = "GDP Per Capita")

set.seed(2018)
e = rnorm(250)
plot(e); abline(h=0)

y = rep(0,250); 
for(t in 1:250){y[t+1]=y[t]+e[t]}
plot(y); abline(h=0)

• The previous picture looks quite realistic.

• But in fact, it is a seemingly random time series.

• It is simulated by some iterative scheme which is completely deterministic.

• Proof: If you copy the code and run in your computer, you will get the same exact pattern. It violates the principle of randomness.

• “Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.” John von Neumann

N = rep(0,250); U = rep(0,250); U[1] = 100 # the seed
for(t in 2:250){  
    U[t] = (1664525 * U[t-1] + 1013904223) %% 2^32
    N[t] = sqrt(2*log(U[t]))*sin(2*pi*U[t])}
hist(N)

• The Motivation of this course.

• The way of understanding the current situation: time and information.