Time Series technical analysis
via new fast estimation
methods
Yan Jungang
A0075380E
Huang Zhaokun A0075386U
Bai Ning
A0075461E
LOGO
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Contents
Introduction
Presentation
Technical analysis
Trading strategies
Forecast foreign exchange rates
 Fundamental Approach
based on a wide range of data regarded as
fundamental economic variables that
determine exchange rates
Fundamental Approach
Steps of fundamental approach
1. starts with a model
2. collects data to estimate the forecasting
equation
3. generation of forecasts
4. evaluation of the forecast
Fundamental Approach
Trading Signal
1. significant difference between the expected
foreign exchange rate and the actual rate
2. a mispricing or a heightened risk premium
3. a buy or sell signal is generated
Forecast foreign exchange rates
 Technical Approach
does not rely on a fundamental analysis of
the underlying economic determinants of
exchange rates or asset prices, but only on
extrapolations of past price trends
Technical Approach
Steps of technical approach
1. recognize the type of trend the market is
2. a level of support
3. form trend lines
Technical Approach
Models
1. Autocorrelations
2. MA model
3. GARCH model
Two kinds of forecasts:
 in-sample:
works within the sample at hand
 out-of-sample
works outside the sample
Linear difference equations
x(t  n)  a1 x(t  n  1)    an x(t )  0
(1)
x(t )  xtrendline (t )  (t )
(2)
 where
xtrendline (t ) is the trendline which
satisfies the above linear equation
  (t ) is the mismatch between the real data
and the trendline
Linear difference equations
Thus
x(t  n)  a1 x(t  n  1)    an x(t )   (t )
 (t )   (t  n)  a1 (t  n  1)    an (t )
we only assume that
lim
 (0)  v(1)     ( N )
(3)
(4)
0
N 1
 t  N , the moving average
N 
MA , N (t ) 
 (t )  v(t  1)     (t  N )
N 1
is close to 0 if N is large enough
Linear difference equations
From equation (4) that  (t ) also satisfies (5)
and (6).
Hence, the finite linear combinations of i.i.d.
zero-mean process, do satisfy almost surely
such a weak assumption.
 Our analysis
 Does not make any difference between nonstationary and stationary time series
Rational generating functions
Consider again Equation (1). The Z-transform
X of x satisfies
z n [ X  x(0)  x(1) z 1    x(n  1) z  ( n 1) ] 
  an 1 z[ X  x(0)]  an X  0
where
n 1
n2
b0 z  b1 z    bn 1 P( z )
X 

n
z    an 1 z  an
Q( z )
P( z ), Q( z )  R( z )
(7)
Parameter identifiability
We introduce the Wronskian matrix
For n real or complex valued functions f1 , ..., f n , which are
n 1times differentiable on an interval I, the Wronskian
W  f1 , ..., f n  as a function on I is defined by
W ( f1 , , f n )( x) 
f1 ( x)
f 2 ( x)
f n ( x)
f1 ( x)
f 2 ( x )
f n ( x )
f1( n 1) ( x)
f 2( n 1) ( x)
f n( n 1) ( x)
,
x  I.
Parameter identifiability
 zn X
z n1 X
 X

n
d ( z n1 X )
dX
 d (z X )

 dz
dz
dz








 d 2 n ( z n X ) d 2 n ( z n 1 X )
d 2n X


dz 2 n
dz 2 n
 dz 2 n
1 

n 1
n2
d (z )
d (z )
d (1) 

dz
dz
dz 

 f ( z n X , ,1)  0



d 2 n ( z n 1 ) d 2 n ( z n 2 )
d 2 n (1) 


2n
2n
2n
dz
dz
dz 
z n1
z n2

The unknown linearly identificable
parameters can be solved by the matrix
linear equation
Methodology
 Data Analysis
 Model Setup
 Example: US Dollar/Euros Exchange Rate
Data Analysis
Sample data:
US Dollar – €uros
Time interval:
1999-01-04 to 2011-03-11
The data can be downloaded from here:
http://www.ecb.int/stats/exchange/eurofxref/html/index.en.html
Data Analysis
 volatility clusters
 volatility evolves over time in a continuous
manner
 volatility varies within some fixed range
 leverage effect
Data Analysis
Stylized-facts of financial return series
The changes in { rt } tend to be
clustered.
The {rt2}
is highly correlated
{ rt } is heavy tailed
stylized-facts
of financial
return series
Data Analysis: Clustered
daily returns of
exchange rate
daily exchange
rate
.
.
Data Analysis: Correlation
H0:
H1:
{Xt}
The log returns are
independent
for some
{Xt2}
The square of log returns
are highly correlated
Data Analysis : Heavy tail
Density function of exchange
rate
Normal-QQ plot
Model Setup
 GARCH Model
.
Model Setup
 Forecast of GARCH Model
.
Example:
US Dollar/Euros Exchange Rate
Estimate of
Estimate
Std. Error
t-value
Pr( >|t| )
μ
7.365e-05
4.584e-05
1.607
0.1081
α0
3.136e-08
1.334e-08
2.350
0.0188
α1
3.147e-02
4.240e-03
7.421
1.16e-13
β1
9.651e-01
4.583e-03
210.588
<2e-16
Std. Errors are based on Hessian.
Significance at 1, 5, 10 percent are indicated by (***), (**), (*).
Example:
US Dollar/Euros Exchange Rate
Residuals Tests
The Ljung-Box Test are performed for standardized residuals and squared
standardized residuals respectively
Trading strategy
Simulate data (ACF)
ACF of historical return
ACF of simulated return
Green:| rt | Red: rt ^2 Blue: rt
Trading strategy
 Take the 10-day historical volatility (HV)
reading.
 Take the 50-day historical volatility (HV)
reading.
If (VAR(10) < 0.5*VAR(50))
Display(“a big move is likely near!”)
Trading strategy
Using historical data to test:
If(VAR(+n)>VAR(-10))
The strategy is efficient
VAR(-10):volatility between trading signal and10 days before the trading signal
VAR(+n):volatility between trading signal and n days after the trading signal
Trading strategy
n
VAR(+n) > VAR(-10)
1
0.4194
2
0.5161
3
0.6419
4
0.7161
5
0.7548
6
0.7871
7
0.8161
8
0.8419
9
0.8484
10
0.8581
Trading strategy
Make an assumption:
when we face the trading signal :

exchange our US dollar to Euro dollar at current time t.

exchange Euro dollar back to US dollar n days after.
By using the historical 3024 days’ exchange rate data,
the program gave us 310 trading signals.
Trading strategy
n
Probability of making profit
1
0.4645
2
0.4645
3
0.4484
4
0.4677
5
0.4806
6
0.4806
7
0.5065
8
0.4968
9
0.5161
10
0.4935
11
0.5129
12
0.5290
13
0.5484
14
0.5290
15
0.5355
Trading strategy
Property of GARCH:
Large shocks tend to be followed by another large
shock;
Small shocks tend to be followed by another small
shock.
Trading signal
Market will volatile in next days
Trading strategy
Problems we faced by now
Know some significance moves are about to take
place.
Not sure what the direction will turn out to be.
using STRADDLE or STRANGLE
Trading strategy
Straddle:
purchase the same number of call and put options at
the same strike price with the same expiration date.
Strangle:
purchase the same number of call and put options at
different strike prices with the same expiration date.
Trading strategy
Steps of trading:
Straddle :
 Buy an ATM (At-The-Money) Put
 Buy an ATM Call
Strangle:
 Buy an OTM (Out-The-Money) Put
 Buy an OTM Call
Trading strategy
Risk and Reward :
 The maximum risk of a Straddle/ Strangle is equal to the
amount that you paid for the two option contracts. If the
stock moves nowhere, and volatility drops to nothing, you
lose.
 The reward is that same as for calls and puts - unlimited.
Trading strategy
Tricks to buy the straddle/
strangle
 Buy options while volatility is relatively slow
 Sell as volatility increase either just before a news report or
soon after.
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