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CFA 2 > Quantitative methods > Flashcards

Quantitative methods Flashcards

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1
Q

Durbin-Watson tests for?

Value 0 =

Value 2 =

DW lower =
DW middle =
DW upper =

A

serial correlation

Value 0 = perfect serial correlation

Value 2 = No serial correlation

DW lower = reject the null
DW middle = inconclusive
DW upper = do not reject the null

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2
Q

T stat =

A

t stat = Coefficient - mean / SE

mean might be zero

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3
Q

R^2 coefficient of determination =

Adjusted R^2 =

Correlation coefficient =

SST =

MSE =

SEE =

A

R^2 = RSS / SST =

Adjusted R^2 = lower than R^2

Square root of R^2

SST = SSE + RSS
Total Variaiton = SSEunexplained + RSSexplained

MSE = SSE / (N-k-1)

SEE = Square root of MSE

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4
Q

What is multicollinearity?

Signs of multicollinearity

Problems caused by it?

Correcting multicollinearity?

A

What is multicollinearity?
Two or more independent variable are highly correlated.

Signs of multicollinearity? High R^2, low t-score, use of a matrix.

Problems caused by it? Estimates of regression coefficients can be unreliable.

Correcting multicollinearity? 1. Remove some of the variables 2. Re-run the model

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5
Q

What is serial correlation?

Test

Correcting for serial correlation?

A

When variables in a time series appear correlated over previous periods of time (used to predict security price changes. Error terms appear correlated. Use DW upper and lower limits to see. Above upper to 2 no serial correlation exists

Test = Durbin Watson

Correcting for serial correlation? Hansen Method adjusts the SE of regression coefficients UPWARDS until there is no serial correlation.

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6
Q

Which model assigns a 1 or 0 to the value of an independent variable?

A

Discriminant analysis models

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7
Q

Hansen method adjusts what/?

A

Adjusts standard errors for both conditional heteroskedasticity and serial correlation

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8
Q

What do probit models test for?

How do they estimate the value of the dependant variable?

What sort of variables can probit test?

A

Test for normal distribution.

Dependant variable is expected to be 1.

Test for qualitative variables

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9
Q

What is homoskedasticity?

What is conditional heteroskedasticity?

What is unconditional heteroskedasticity?

A

Variance of the error term is constant across all observations

Variance of error terms changes in a systematic manner that is correlated with values of the independant variable

Variance of the error term changes in an unsystematic way that is not correlated with the independent variables.

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10
Q

Dicky Fuller tests for?

Durbin Watson tests for?

Breusch Pagen tests for?

A

Dicky Fuller tests for Non-stationarity

Durbin Watson tests for serial correlation

Breusch Pagen tests for conditional Heteroskedasticity using chi-squared.

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11
Q

Y = b0 + b1X1 + b2X2 + error term
b0 =
b1X1 =
b2X2 =

A 
Y = What you are forecasting
b0 = Intercept
b1X1 = Independent variable x regression coefficient
b2X2 = Independent variable x regression coefficient
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12
Q

T-stat =

A

Coefficient - mean / SE

Coefficient could be advertising or hours worked

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13
Q

F Stat =

F Table =

F stat > F table

A

F Stat = (RSS/K) / (SSE/n-k-1) or RSS/K

F Table = k / n-k-1

F stat > F table then one independent variable explains variance of the dependent variable

k = number of independant variables ie advertising and hours worked k = 2
n = number of data sets usually years
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14
Q

How many dummy variables needed for 4 quarters?

A

Dummy variables is ONE less. So 3.

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15
Q

Mean reverting level =

A

MRL = b0 / 1 - b1

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16
Q

AR Model with 101 observations, SE =

What test is used and what level shows AR model is not correctly specified? =

Less than this level shows?

A

SE = 1 / Square root of n

T-distribution is used at 5%, above 2 is mis-specified.

Less than this level shows that it is specified correctly.

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17
Q

Random walk =
Random walk unit root lag coefficient b1 =

Mean Reverting =

A

Random walk = Is Significant
lag coefficient = 1

Mean Reverting = Not significant

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18
Q

ARCH Errors =

A

error terms are heteroskedastic and SE of regression coefficient is incorrect.

Signs include lagged variable being significantly different to zero in the model.

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19
Q

Dicky fuller
a) has a problem with the unit root

b) does not have a problem with the unit root

A

Dicky fuller
a) has a problem with the unit root = accept the null

b) does not have a problem with the unit root = reject the null as they are cointegrated.

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20
Q

First differenced random walk =

A

Yt = b0 + error term

Where Yt = Xt - Xt-1

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21
Q

A lag coefficient > 1 concludes

A

Lag coefficient > 1 = The model has an explosive root.

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22
Q

First differencing =

A

Allows analysts to conclude original time series are random walk

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23
Q

Dendogram hierarchical clustering with short dendrites indicates?

A

Denrites are vertical lines and shorter lines indicate similar clusters of data.

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24
Q

Supervised learning

vs

Unsupervised learning

A

Supervised learning uses prelabelled data such as fraudulent activities

vs

Unsupervised learning does not use pre-labelled data and algorithms try to describe the data.

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25
Q

Bagging aka bootstrapping samples original data or old data? What type of samples are used?

A

Bagging uses original data and reduces teh incidence of overfitting. New data bags are produced from random sampling.

26
Q

What is divisive hierarchical clustering?

Supervised or unsupervised?

A

Begins with one cluster divided into smaller clusters.
Top down process until each cluster has only one observation

Supervised learning

27
Q

What is dimension reduction?

Supervised or Unsupervised?

A

Identifying major correlated data factors and reducing them into fewer uncorrelated variables, a form of unsupervised learning.

28
Q

Penalised regression =

A

Adds a penalty as the number of included

29
Q

What is a classification and Regression Tree? CART
What does it minimise?
Supervised or Unsupervised?

A

Splitting data into two categories using decision trees and binary branching to classify observations. It makes no assumptions about data sets.

They are used to minimise classification errors.

CART is a form of supervised machine learning

30
Q

Ensemble learning

A

Ensemble learning results in more accurate and more stable models. Ensemble learning can aggregate both heterogenous and homogenous learners.

31
Q

Base error

Bias error

Variance error

A

Base error arises from randomness of data

Bias error arises when a model does not fit training data well

Variance error arises when the model fits too well creating noise.

32
Q

What is overfitting?

What is underfitting?

Which is more susceptible to linner and non linnear functions?

A

When a machine learning model learns the input and target data set too precisely. A non-linnear function error.

The opposite and suseptible to linnear function errors

33
Q

Centroids k-means clustering?

What does it require?

A

Centroids k-means clustering is when an algorithm iterates until no observations are moved to new clusters.

It requires a define number of groups ‘k’ being the number of data inputs.

34
Q

What is an Eigen value?

A

The proportion of total variance explained by an eigenvector from the initial data.

35
Q

Agglomorate clustering =

Divisive clustering =

How many observations in the final cluster for each?

A

Agglomorate clustering is bottom up and final clusters contain all items/observations. Clusters increase in size.

Divisive clustering = Top down, final cluster contains one observation

36
Q

k-fold cross validation gives an estimate of?

A

k-fold cross validation gives an estimation of ‘ou-of-sample’ errors

37
Q

Random forrest classifier?

A

classification trees undertake classification to reduce a problem of overfitting.

38
Q

ML Regression problem target is:

ML classification problem target data is:

A

ML Regression problem target is continuous

ML classification problem target data is either categorical or ordinal

39
Q

Which neural layer does learning take place?

Which element of a neural network increases/decrease strength of input?

A

Hidden layer

The activation function increases/decreases strength of input.

40
Q

Deep learning nets aka:

supervised or unsupervised?

What separates them?

A

Deep learning nets aka Artificial Neural Networks

BOTH supervised or unsupervised!

What separates them is the many hidden layers (at least three)

41
Q

Activation of a neural network =

A

Non-linner function which adjusts the strength of an unput.

42
Q

Number of nodes in a Deep Learning Net DLN is determined how?

A

The number of nodes is determined by the number of dimensions in a feature set.

43
Q

Training a neural network is forward or backward?

A

Both forward and backward training is used for a neural network.

44
Q

Different between reinforcement and supervised learning?

A

Reinforcement learning has neither labelled data nor can it give instantaneous feedback.

45
Q

Data curation stage includes

Data exploration includes

A

Web spidering which gathers raw data.

Data exploration feature selection for out of sample data and Feature engineering for optimising selected features.

46
Q 
Mutual Information
Token dollar appearing in all class of text is assigned a:

Token dollar appearing in one class of text is assigned a:

A 
Mutual Information
Token dollar appearing in all class of text is assigned a = 0

Token dollar appearing in one class of text is assigned a = 1

47
Q

Stages of data exploration =

A
  1. Data Exploration (model features engineered)
  2. Feature selection
  3. Feature engineering
48
Q

Structured or Unstructured for:

Standard ML models

Text ML models

A

Standard ML models = Structured data

Text ML models = Unstructured data

49
Q

ML Iterative process
Step 1
Step 2

A

ML Iterative process
Step 1 = Conceptualization
Step 2 = Reconceptualization

50
Q

4 V’s of big data =

A

Volume (quantity of data)
Variety (array of data)
Velocity (speed of data creation)
Veracity (reliability/credibility of data)

51
Q

Trimming

vs

Filtration

vs

Winsorisation

A

Trimming removes outliars

vs

Filtration removes unrequired data

vs

Winsorigation is data wrangling (preparing data for ML model) where outliars high and low are replaced.

52
Q

Precision of data formula =

Recall data formula =

Accuracy formula =

FP =

FN =

Given True Positive TP, False Positive FP, False negatvie FN, and True Negative TN.

A

Precision of data formula = TP / TP + FP

Recall data formula = TP / TP + FN

Accuracy formula = TP + TN / (TP + FP + TN + FN)

FP = Type 1 error

FN = Type 2 error

53
Q

Area Under Curve value normal:

AUC showing random guessing and higher convexity =

A

Area Under Curve value normal: 0.5

AUC showing random guessing and higher convexity = > 0.5 ie 0.67

54
Q

3 stages of model training =

Small data set more likely of:

A

3 stages of model training =

  1. Method selection
  2. Performance evaluation
  3. Tuning

Underfitting more likely from small data sets

55
Q

Main advantage of a simulation model over a decision tree?

3 data types of simulation data =

A

Simulations provide FULL distribution in addition to expected values.

3 data types of simulation data =
1 Historical data
2. Cross sectional data
3. Adopting a statistical distribution.

56
Q

Steps in simulations

What is a probabilistic variable

A
  1. Determine probablistic vairables
  2. Define probability distributions
  3. Check for correlations

What is a probabilistic variable is a trade between number of variables and complexity of the simulation.

57
Q

Which model below better copes with sequential risk and concurrent risk?

Simulations =
Decision trees =
Scenario analysis =

A

Simulations = Accomodates both sequential and concurrent
Decision trees = better accommodates sequential risk
Scenario analysis =better accommodates concurrent risk

58
Q

random walk signs

Test for Random walk on an AR(1) model =

A

Slope coefficient is close to value: 1

An AR(1) model is tested using the Dicky fuller test and it tests for random walk.

59
Q

confidence internal =

90%
95%
99%

A 
90% = 1.6
95% = 2
99% = 2.6

Coefficient +/- SE x confidence interval

60
Q

High bias error
High variance error

Under or over fitted?

A

High bias error indicates underfitting a dataset

High variance error indicates overfitting a dataset

61
Q

Precision =

Recall =

Accuracy =

F1 =

A

Precision = TP / TP + FP

Recall = TP / TP + FN

Accuracy = TP + TN / TP + TN + FP + FN

F1 = 2 x P x R / (P + R)

62
Q

What is data wrangling

A

Text wrangling (preprocessing) can be essential in making sure you have the best data to work with. it requires performing normalization and involves the following:
lowercasing
removing stop words such as “the” and “a” because of their many occurrences.
stemming: cutting down a token to its root stem.

CFA 2 (10 decks)

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