Ac.F633代做、Python程序语言代写

日期：2024-04-08 07:48

Ac.F633 - Python Programming Final Individual Project

Ac.F633 - Python Programming for Data Analysis

Manh Pham

Final Individual Project

20 March 2024 noon/12pm to 10 April 2024 noon/12pm (UK time)

This assignment contains one question worth 100 marks and constitutes 60% of the

total marks for this course.

You are required to submit to Moodle a SINGLE .zip folder containing a single Jupyter Notebook .ipynb file OR a single Python script .py file, together with

any supporting .csv files (e.g. input data files. However, do NOT include the

‘IBM 202001.csv.gz’ data file as it is large and may slow down the upload and submission) AND a signed coursework coversheet. The name of this folder should be

your student ID or library card number (e.g. 12345678.zip, where 12345678 is your

student ID).

In your answer script, either Jupyter Notebook .ipynb file or Python .py file, you

do not have to retype the question for each task. However, you must clearly label

which task (e.g. 1.1, 1.2, etc) your subsequent code is related to, either by using a

markdown cell (for .ipynb file) or by using the comments (e.g. #1.1 or ‘‘‘1.1’’’

for .py file). Provide only ONE answer to each task. If you have more than one

method to answer a task, choose one that you think is best and most efficient. If

multiple answers are provided for a task, only the first answer will be marked.

Your submission .zip folder MUST be submitted electronically via Moodle by the

10 April 2024 noon/12pm (UK time). Email submissions will NOT be considered. If you have any issues with uploading and submitting your work to Moodle,

please email Carole Holroyd at c.holroyd@lancaster.ac.uk BEFORE the deadline

for assistance with your submission.

The following penalties will be applied to all coursework that is submitted after the

specified submission date:

Up to 3 days late - deduction of 10 marks

Beyond 3 days late - no marks awarded

Good Luck!

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Ac.F633 - Python Programming Final Individual Project

Question 1:

Task 1: High-frequency Finance (Σ = 30 marks)

The data file ‘IBM 202001.csv.gz’ contains the tick-by-tick transaction data for

stock IBM in January 2020, with the following information:

Fields Definitions

DATE Date of transaction

TIME M Time of transaction (seconds since mid-night)

SYM ROOT Security symbol root

EX Exchange where the transaction was executed

SIZE Transaction size

PRICE Transaction price

NBO Ask price (National Best Offer)

NBB Bid price (National Best Bid)

NBOqty Ask size

NBBqty Bid size

BuySell Buy/Sell indicator (1 for buys, -1 for sells)

Import the data file into Python and perform the following tasks:

1.1: Write code to perform the filtering steps below in the following order: (15 marks)

F1: Remove entries with either transaction price, transaction size, ask price,

ask size, bid price or bid size ≤ 0

F2: Remove entries with bid-ask spread (i.e. ask price - bid price) ≤ 0

F3: Aggregate entries that are (a) executed at the same date time (i.e. same

‘DATE’ and ‘TIME M’), (b) executed on the same exchange, and (c) of

the same buy/sell indicator, into a single transaction with the median

transaction price, median ask price, median bid price, sum transaction

size, sum ask size and sum bid size.

F4: Remove entries for which the bid-ask spread is more that 50 times the

median bid-ask spread on each day

F5: Remove entries with the transaction price that is either above the ask

price plus the bid-ask spread, or below the bid price minus the bid-ask

spread

Create a data frame called summary of the following format that shows the

number and proportion of entries removed by each of the above filtering steps.

The proportions (in %) are calculated as the number of entries removed divided

by the original number of entries (before any filtering).

F1 F2 F3 F4 F5

Number

Proportion

Here, F1, F2, F3, F4 and F5 are the columns corresponding to the above 5

filtering rules, and Number and Proportion are the row indices of the data

frame.

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Ac.F633 - Python Programming Final Individual Project

1.2: Using the cleaned data from Task 1.1, write code to compute Realized

Volatility (RV), Bipower Variation (BV) and Truncated Realized Volatility

(TRV) measures (defined in the lectures) for each trading day in the sample

using different sampling frequencies including 1 second (1s), 2s, 3s, 4s, 5s, 10s,

15s, 20s, 30s, 40s, 50s, 1 minute (1min), 2min, 3min, 4min, 5min, 6min, 7min,

8min, 9min, 10min, 15min, 20min and 30min. The required outputs are 3

data frames RVdf, BVdf and TRVdf (for Realized Volatility, Bipower Variation

and Truncated Realized Volatility respectively), each having columns being

the above sampling frequencies and row index being the unique dates in the

sample. (10 marks)

1.3: Use results in Task 1.2, write code to produce a 1-by-3 subplot figure that

shows the ‘volatility signature plot’ for RV, BV and TRV. Scale (i.e. multiply)

the RVs, BVs and TRVs by 104 when making the plots. Your figure should

look similar to the following.

0 500 1000 1500

Sampling frequency (secs)

1.0

1.5

2.0

2.5

A

v

era

g

e

d

R

V (x10

4

)

RV signature plot

0 500 1000 1500

Sampling frequency (secs)

0.6

0.8

1.0

1.2

1.4

A

v

era

g

e

d

B

V (x10

4

)

BV signature plot

0 500 1000 1500

Sampling frequency (secs)

0.5

0.6

0.7

0.8

0.9

1.0

A

v

era

g

e

d

T

R

V (x10

4

)

TRV signature plot

(5 marks)

Task 2: Return-Volatility Modelling (Σ = 25 marks)

Refer back to the csv data file ‘DowJones-Feb2022.csv’ that lists the constituents of the Dow Jones Industrial Average (DJIA) index as of 9 February

2022 that was investigated in the group project. Import the data file into

Python.

Using your student ID or library card number (e.g. 12345678) as a random

seed, draw a random sample of 2 stocks (i.e. tickers) from the DJIA index

excluding stock DOW.1

Import daily Adjusted Close (Adj Close) prices for

both stocks between 01/01/2010 and 31/12/2023 from Yahoo Finance. Compute the log daily returns (in %) for both stocks and drop days with NaN

returns. Perform the following tasks.

2.1: Using data between 01/01/2010 and 31/12/2020 as in-sample data, write

code to find the best-fitted ARMA(p, q) model for returns of each stock that

minimizes AIC, with p and q no greater than 3. Print the best-fitted ARMA(p, q)

output and a statement similar to the following for your stock sample.

Best-fitted ARMA model for WBA: ARMA(2,2) - AIC = 11036.8642

Best-fitted ARMA model for WMT: ARMA(2,3) - AIC = 8810.4277 (5 marks)

1DOW only started trading on 20/03/2019

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Ac.F633 - Python Programming Final Individual Project

2.2: Write code to plot a 2-by-4 subplot figure that includes the following diagnostics for the best-fitted ARMA model found in Task 2.1:

Row 1: (i) Time series plot of the standardized residuals, (ii) histogram of

the standardized residuals, fitted with a kernel density estimate and the

density of a standard normal distribution, (iii) ACF of the standardized

residuals, and (iv) ACF of the squared standardized residuals.

Row 2: The same subplots for the second stock.

Your figure should look similar to the following for your sample of stocks.

Comment on what you observe from the plots. (6 marks)

2010 2012 2014 2016 2018 2020

Date

8

6

4

2

0

2

4

6

ARMA(2,2) Standardized residuals-WBA

3 2 1 0 1 2 3

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Density

Distribution of standardized residuals

N(0,1)

0 5 10 15 20 25 30 35

1.00

0.75

0.50

0.25

0.00

0.25

0.50

0.75

1.00

ACF of standardized residuals

0 5 10 15 20 25 30 35

1.00

0.75

0.50

0.25

0.00

0.25

0.50

0.75

1.00 ACF of standardized residuals squared

2010 2012 2014 2016 2018 2020

Date

7.5

5.0

2.5

0.0

2.5

5.0

7.5

ARMA(2,3) Standardized residuals-WMT

3 2 1 0 1 2 3

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Density

Distribution of standardized residuals

N(0,1)

0 5 10 15 20 25 30 35

1.00

0.75

0.50

0.25

0.00

0.25

0.50

0.75

1.00

ACF of standardized residuals

0 5 10 15 20 25 30 35

1.00

0.75

0.50

0.25

0.00

0.25

0.50

0.75

1.00 ACF of standardized residuals squared

2.3: Use the same in-sample data as in Task 2.1, write code to find the bestfitted AR(p)-GARCH(p

∗

, q∗

) model with Student’s t errors for returns of each

stock that minimizes AIC, where p is fixed at the AR lag order found in

Task 2.1, and p

∗ and q

∗ are no greater than 3. Print the best-fitted AR(p)-

GARCH(p

∗

, q∗

) output and a statement similar to the following for your stock

sample.

Best-fitted AR(p)-GARCH(p*,q*) model for WBA: AR(2)-GARCH(1,1) - AIC

= 10137.8509

Best-fitted AR(p)-GARCH(p*,q*) model for WMT: AR(2)-GARCH(3,0) - AIC

= 7743.4547 (5 marks)

2.4: Write code to plot a 2-by-4 subplot figure that includes the following diagnostics for the best-fitted AR-GARCH model found in Task 2.3:

Row 1: (i) Time series plot of the standardized residuals, (ii) histogram of

the standardized residuals, fitted with a kernel density estimate and the

density of a fitted Student’s t distribution, (iii) ACF of the standardized

residuals, and (iv) ACF of the squared standardized residuals.

Row 2: The same subplots for the second stock.

Your figure should look similar to the following for your sample of stocks.

Comment on what you observe from the plots. (6 marks)

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Ac.F633 - Python Programming Final Individual Project

2010 2012 2014 2016 2018 2020

Date

10.0

7.5

5.0

2.5

0.0

2.5

5.0

7.5

AR(2)-GARCH(1,1) Standardized residuals-WBA

3 2 1 0 1 2 3

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Density

Distribution of standardized residuals

t(df=3.7)

0 5 10 15 20 25 30 35

1.00

0.75

0.50

0.25

0.00

0.25

0.50

0.75

1.00

ACF of standardized residuals

0 5 10 15 20 25 30 35

1.00

0.75

0.50

0.25

0.00

0.25

0.50

0.75

1.00 ACF of standardized residuals squared

2010 2012 2014 2016 2018 2020

Date

10

5

0

5

10

AR(2)-GARCH(3,0) Standardized residuals-WMT

3 2 1 0 1 2 3

0.0

0.1

0.2

0.3

0.4

0.5

Density

Distribution of standardized residuals

t(df=3.9)

0 5 10 15 20 25 30 35

1.00

0.75

0.50

0.25

0.00

0.25

0.50

0.75

1.00

ACF of standardized residuals

0 5 10 15 20 25 30 35

1.00

0.75

0.50

0.25

0.00

0.25

0.50

0.75

1.00 ACF of standardized residuals squared

2.5: Write code to plot a 1-by-2 subplot figure that shows the fitted conditional

volatility implied by the best-fitted AR(p)-GARCH(p

∗

, q∗

) model found in

Task 2.3 against that implied by the best-fitted ARMA(p, q) model found in

Task 2.1 for each stock in your sample. Your figure should look similar to the

following.

2010

2012

2014

2016

2018

2020

Date

1

2

3

4

5

6

7

Fitted conditional volatility for stock WBA

AR(2)-GARCH(1,1)

ARMA(2,2)

2010

2012

2014

2016

2018

2020

Date

1

2

3

4

5

6

Fitted conditional volatility for stock WMT

AR(2)-GARCH(3,0)

ARMA(2,3)

(3 marks)

Task 3: Return-Volatility Forecasting (Σ = 25 marks)

3.1: Use data between 01/01/2021 and 31/12/2023 as out-of-sample data, write

code to compute one-step forecasts, together with 95% confidence interval

(CI), for the returns of each stock using the respective best-fitted ARMA(p, q)

model found in Task 2.1. You should extend the in-sample data by one observation each time it becomes available and apply the fitted ARMA(p, q) model

to the extended sample to produce one-step forecasts. Do NOT refit the

ARMA(p, q) model for each extending window.2 For each stock, the forecast

output is a data frame with 3 columns f, fl and fu corresponding to the

one-step forecasts, 95% CI lower bounds, and 95% CI upper bounds. (5 marks)

3.2: Write code to plot a 1-by-2 subplot figure showing the one-step return

forecasts found in Task 3.1 against the true values during the out-of-sample

2Refitting the model each time a new observation comes generally gives better forecasts. However,

it slows down the program considerably so we do not pursue it here.

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Ac.F633 - Python Programming Final Individual Project

period for both stocks in your sample. Also show the 95% confidence interval

of the return forecasts. Your figure should look similar to the following.

2021-05

2021-09

2022-01

2022-05

2022-09

2023-01

2023-05

2023-09

Date

10.0

7.5

5.0

2.5

0.0

2.5

5.0

7.5

ARMA(2,2) One-step return forecasts - WBA

Observed

Forecasts

95% IC

2021-05

2021-09

2022-01

2022-05

2022-09

2023-01

2023-05

2023-09

Date

12.5

10.0

7.5

5.0

2.5

0.0

2.5

5.0

ARMA(2,3) One-step return forecasts - WMT

Observed

Forecasts

95% IC

(3 marks)

3.3: Write code to produce one-step analytic forecasts, together with 95%

confidence interval, for the returns of each stock using respective best-fitted

AR(p)-GARCH(p

∗

, q∗

) model found in Task 2.3. For each stock, the forecast

output is a data frame with 3 columns f, fl and fu corresponding to the

one-step forecasts, 95% CI lower bounds, and 95% CI upper bounds. (4 marks)

3.4: Write code to plot a 1-by-2 subplot figure showing the one-step return

forecasts found in Task 3.3 against the true values during the out-of-sample

period for both stocks in your sample. Also show the 95% confidence interval

of the return forecasts. Your figure should look similar to the following.

2021-05

2021-09

2022-01

2022-05

2022-09

2023-01

2023-05

2023-09

Date

15

10

5

0

5

10

15

AR(2)-GARCH(1,1) One-step return forecasts - WBA

Observed

Forecasts

95% IC

2021-05

2021-09

2022-01

2022-05

2022-09

2023-01

2023-05

2023-09

Date

15

10

5

0

5

10

15

AR(2)-GARCH(3,0) One-step return forecasts - WMT

Observed

Forecasts

95% IC (3 marks)

3.5: Denote by et+h|t = yt+h − ybt+h|t

the h-step forecast error at time t, which

is the difference between the observed value yt+h and an h-step forecast ybt+h|t

produced by a forecast model. Four popular metrics to quantify the accuracy

of the forecasts in an out-of-sample period with T

′ observations are:

1. Mean Absolute Error: MAE = 1

T′

PT

′

t=1 |et+h|t

|

2. Mean Square Error: MSE = 1

T′

PT

′

t=1 e

2

t+h|t

3. Mean Absolute Percentage Error: MAPE = 1

T′

PT

′

t=1 |et+h|t/yt+h|

4. Mean Absolute Scaled Error: MASE = 1

T′

PT

′

t=1

et+h|t

1

T′−1

PT′

t=2 |yt − yt−1|

.

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Ac.F633 - Python Programming Final Individual Project

The closer the above measures are to zero, the more accurate the forecasts.

Now, write code to compute the four above forecast accuracy measures for

one-step return forecasts produced by the best-fitted ARMA(p,q) and AR(p)-

GARCH(p

∗

,q

∗

) models for each stock in your sample. For each stock, produce

a data frame containing the forecast accuracy measures of a similar format

to the following, with columns being the names of the above four accuracy

measures and index being the names of the best-fitted ARMA and AR-GARCH

model:

MAE MSE MAPE MASE

ARMA(2,2)

AR(2)-GARCH(1,1)

Print a statement similar to the following for your stock sample:

For WBA:

Measures that ARMA(2,2) model produces smaller than AR(2)-GARCH(1,1)

model:

Measures that AR(2)-GARCH(1,1) model produces smaller than ARMA(2,2)

model: MAE, MSE, MAPE, MASE. (5 marks)

3.6: Using a 5% significance level, conduct the Diebold-Mariano test for each

stock in your sample to test if the one-step return forecasts produced by the

best-fitted ARMA(p,q) and AR(p)-GARCH(p

∗

,q

∗

) models are equally accurate

based on the three accuracy measures in Task 3.5. For each stock, produce a

data frame containing the forecast accuracy measures of a similar format to

the following:

MAE MSE MAPE MASE

ARMA(2,2)

AR(2)-GARCH(1,1)

DMm

pvalue

where ‘DMm’ is the Harvey, Leybourne & Newbold (1997) modified DieboldMariano test statistic (defined in the lecture), and ‘pvalue’ is the p-value associated with the DMm statistic. Draw and print conclusions whether the bestfitted ARMA(p,q) model produces equally accurate, significantly less accurate

or significantly more accurate one-step return forecasts than the best-fitted

AR(p)-GARCH(p

∗

,q

∗

) model based on each accuracy measure for your stock

sample.

Your printed conclusions should look similar to the following:

For WBA:

Model ARMA(2,2) produces significantly less accurate one-step return

forecasts than model AR(2)-GARCH(1,1) based on MAE.

Model ARMA(2,2) produces significantly less accurate one-step return

forecasts than model AR(2)-GARCH(1,1) based on MSE.

Model ARMA(2,2) produces significantly less accurate one-step return

forecasts than model AR(2)-GARCH(1,1) based on MAPE.

Model ARMA(2,2) produces significantly less accurate one-step return

forecasts than model AR(2)-GARCH(1,1) based on MASE. (5 marks)

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Ac.F633 - Python Programming Final Individual Project

Task 4: (Σ = 20 marks)

These marks will go to programs that are well structured, intuitive to use (i.e.

provide sufficient comments for me to follow and are straightforward for me

to run your code), generalisable (i.e. they can be applied to different sets of

stocks (2 or more)) and elegant (i.e. code is neat and shows some degree of

efficiency).

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