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CFA L2 Matheus > 3. Quantitative Methods > Flashcards

3. Quantitative Methods Flashcards

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1
Q

Sum of Squared Errors (Definition)

A

Difference between Yi and Ŷ (observation and estimate)

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2
Q

Sum of Squared Regression (Definition)

A

Difference between Ŷ and Mean of Y (regression and best descriptive estimator)

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3
Q

SSR (#Degrees of Freedom)

A

k (# parameters of X estimated in the regression)

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4
Q

SSE (#Degrees of Freedom)

A

n-k-1 (N - estimators of X - intercept)

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5
Q

SST (#Degrees of Freedom)

A

(n-1)

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6
Q

Mean Squared of Regression (Formula)

A

MSR = SSR/k

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7
Q

Mean Squared of Error (Formula)

A

MSE = SSE/(n-k-1)

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8
Q

Squared Error of Estimate (SEE Formula)

A

SSE = √MSE

The lower, the more accurate the model is

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9
Q

F Test

A

F = MSR / MSE (testar a diferença entre a regressão em comparação com o erro)

DF @ K numerator (horizontal)
DF @ N-K-1 denominator (vertical)

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10
Q

Regression Assumptions

A
  1. Linearity
  2. Homoscedasticity (var ε same across observations). Muita ou pouca VOL.
  3. Pairs X and Y are independent (if not, there is serial correlation)
  4. a. Residuals are independently distributed
  5. b. Residuals’ distribution is Normal
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11
Q

B0 (Intercept Test)

A

T-Test = (B1 est - B1 hipótese) / SB1

One-tail or Two-tails @ df = (n-k-1), as I am using error as a denominator

Sb1 = SEE / Sum of Sqaures of (Obs X - Mean X)

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12
Q

Dummy Variable

A

Y = b0 + b1*Dummy

Dummy = 0 or 1

If Dummy = 0, then Y = b0 = mean

If Dummy = 1, then Y = b0 + b1

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13
Q

Confidence Interval (Formula)

A

Interval = Ŷ ± T-Critical * Sf

Ŷ = Calculate using regression
Sf = Std Error of Forecast =
Sf = SEE² * [1 + 1/n * [(X-Mean)²/(n-1*Sx²)]
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14
Q

R² (Formula)

A

R² = SSR/SST = Measure of Fit

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15
Q

Regression Types

A
  1. Log-Lin = lnY = b0+b1X1
  2. Log-Log = lnY = b0 + b1*(lnX1)
  3. Lin-Log = Y = b0 + b1*(lnX1)
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16
Q

Multiple Regression Assumptions

A
  1. X e Y are linear
  2. IVs (X) are not random
  3. E (ε | X1, X2, Xk) = 0
  4. E (ε²) = Variância e é igual para todas as observações
  5. E (erro1, erro2) = 0, erro não é correlacionado
  6. Erro é distr. ~N
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17
Q

F-statistic for Multiple (Hypothesis)

A

H0: B1 = B2 = B3 = 0
H1: At least one ≠ 0

One-Tailed Test @
DF Numerator = K = Horizontal
DF Denominator = (N-K-1) = Vertical

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18
Q

R² Adjusted (Formula)

A

Adj. R² = 1 - [(n-1)/(n-k-1)] * [1-R²]

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19
Q

Multicolinearity (Definition)

A

B1 e B2 t-tests are not relevant, but F-test is

Reason: Two IVs are highly correlated
Detection: ↑ R² and ↑ F-test, but ↓ B0
Correction: Omit one variable
Consequence: ↑ SE = ↓ F test

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20
Q

Heteroskedasticity (Definition)

A

Var of ε changes across observations

Unconditional: Var (ε) NOT correlated w/ IVs
Conditional: Var (ε) IS correlated w/ IVs

Correction:

  • Robust Std Errors
  • Generalized Least Squares
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21
Q

Heteroskedasticity (Test)

A

Breusch Pagan Test (OH NO)

H0: NO conditional
H1: Conditional

Test = n * R²*ε @ Chi Squared Table

Regress the error on the IVs

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22
Q

Hansen Method (Definition)

A

Preferred if (i) SC or (ii) SC + Heteroskedasticity

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23
Q

Serial Correlation (Definition)

A
  • Errors are explained by similar reasons
  • ↓ SEE = ↑ F-test
  • Violates Independence of Pairs (X and Y)
  • Se o erro anterior é positivo, chance do erro seguinte ser positivo é de fato mais alta
  • If IV = Y lagged, then B0 will not be valid
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24
Q

Test for Serial Correlation

A

Durbin Watson (Deutsche Welle)

H0: DW = 2 (No Correl)
H1: DW ≠ 2 (Correl)

Test = 2*(1-r)
DF = K and N items

Correction: (i) Modified SEs,

(ii) Modify Regression Equation
(iii) Include seasonal term

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25
Q

Hansen or White Method (Criteria)

A

If only Hetero: White SEs
If only SC: Hansen
If both: Hansen is preferred

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26
Q

Standard Error of Residuals (Formula)

A

SE Residuals = 1 /√T, where T = # observations

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27
Q

Misspecifications of Model (List)

A
  1. Data Mining
  2. Functional Form (Linear, Log, Diff Samples)
  3. Parsimonious IVs
  4. Examine violations before accepting
  5. Tested out of sample
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28
Q

Logit Regressions

A

Ln (Odds) = B0 + B1X1 + BnXn + ε

Estima a máxima chance de o sample ter acontecido

Slope = Chg Log Odds of event happening

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29
Q

Odds (Formula)

A

Odds = p % / (1 - p)

ln (p/(1-p)) = b0+b1X1 + ε

p = (e^A) / (1 + e^A), onde A = equação

30
Q

Time Series Analysis

A

Yt = B0 + B1t + εt, where IV is Time

Often have Serial Correlation, so test for Durbin Watson

31
Q

AR Model (Concept)

A

Xt = B0 + B1Xt-1 + ε (AR1)

  • Regress X in its past values
  • Se B1 < 1, modelo é mean reverting
  • Não pode usar DW
  • Tem que usar t = Autocorrel / (1 /√T)
32
Q

AR (2) Model Structure

A

AR(2) Model Y(t) = b0 + b1* y(t-1) + b2*y(t-2)

33
Q

Covariance Stationary Model

A

(a) Mean = fixa
(b) Variance = constante
(c) Cov(Yt,Yt-s)

Todos constantes e finitos

34
Q

Mean Reverting Level (Formula)

A

Xt = b0 / (1 - b1)

35
Q

Compare 2 models (in terms of forecasting power)

A
  • In-Sample forecasts: Predicted v. Observed
  • Out of Sample:
    Use RMSE = √(Soma Act - Forecast)²/ n
    RMSE = menor melhor
36
Q

Random Walk (Definition)

A
  • X is explained by a sum of errors
  • AR model where B0 = 0 and B1 = 1, then not mean reverting level
  • No Mean Reverting
  • No Cte Variance
37
Q

Random Walk w/ Drift (Definition)

A
  • Intercept is not ZERO (B0 ≠ 0)

- B1 is still 1

38
Q

Seasonality (Definition)

A
  • One of autocorrelation tests for IVs in AR model will be very significative
  • Correction: include a seasonal lag
39
Q

ARCH Model (Definition)

A
  • It means testing to check if an AR model has conditional heteroskedasticity
  • Is ε correlated to X1, X2? This is the question
40
Q

ARCH Model (Steps)

A
  1. Regress ε² (Var) on a1 *ε² (t-1)
  2. Test for a1 = 0 / a1 ≠ 0
  3. H0 is good. H1 means it has Cond. Hetero
  4. If it has CH, use Generalized Least Squares
41
Q

Regression using > 1 Time Series (concept)

A

Y (Time Series #1) = f (X = other Time Series #2)

42
Q

Many Time Series: when can I use?

A
  • If BOTH ARE cov stationary, or

- If BOTH are NOT, but ARE cointegrated (share a common trend)

43
Q

Big Data Learning Types

A
  • Supervised: Labeled Data

- Unsupervised: Data is NOT labeled

44
Q

Big Data Variables (Types)

A
  • Feature (Input)

- Target (Output)

45
Q

Big Data Problem Categories

A
  • Regress (Continuous Target)

- Classification (Categorical / Order)

46
Q

Overfit Problem (Definition)

A
  • Treat noise as parameter
47
Q

Samples Used to Test Model (Types)

A
  1. Training Sample
  2. Validation Sample
  3. Test Sample
48
Q

Big Data Error (Types)

A

Bias Error: Underfitting (acertar pouco in-sample)
Variance Error: Overfit (acerta d+ in-sample, ruim na hora de generalizar)
Base Error: Noise

49
Q

Complexity Problem Solving

A
  1. Reduce Complexity
  2. Cross Validation (invert training and validation samples)
  3. K-Fold Cross Validation: let (n-1) and test in the last one to avoid sample error
50
Q

Supervised Learning Methods

A
  • CART
  • K-nearest neighbors
  • LASSO (elimina IVs + hyperparameter)
  • Penalized Regression (hyperparemeter)
  • SVM
  • Calvin Klein Luan Panisson
51
Q

Unsupervised Learning Methods

A
  • PCA (reduce dimensionality)
  • Clustering
  • Neural Networks (desdobra em Deep Learning Nets e Reinforcement Learning)
52
Q

Regress & Classification Methods (which work for both)

A
  • Neural Networks
  • Deep Learning Nets
  • Reinforced Learning
53
Q

Regression Methods

A

Not Linear:

  • CART
  • Random Forest
  • Neural Nets

Linear: Regression

54
Q

Classification Methods

A

Labeled:

  • Complex: CART, Random Forest
  • Normal: KNN, SVM

Unlabeled:

  • Complex: Neural Nets
  • Normal: K-means (# categories known) or Hierarchical Clustering
55
Q

Structured Data Cleasing (Processes)

A
  • Incomplete
  • Inconsistent
  • Inaccurate
  • Invalid
  • Non-Uniform
  • Duplicate
56
Q

Unstructured Data Cleasing (Processes)

A
  • Remove HTML tags
  • Lowercase
  • Remove stop words
  • STEM
  • Lemmarize
57
Q

Big Data Projects Steps

A
  1. Conceptualize
  2. Data Collection
  3. Data Preparation (Clean, Wrangle)
  4. Data Exploration
  5. Model Training
58
Q

Stem (Definition)

A

Data Cleansing:

  • From all derived to root word
  • Connection / Connecting -> Connect (root)
59
Q

Lemmatize (Definition)

A

Data Cleansing:

  • Remove endings if the base is in a dictionary
  • More costly and advanced
  • Takes context / speech to change data
60
Q

Data Processing / Wrangle (Types)

A
  • Structured: Extract, Filter, Aggregate, Convert (Trim, Scale, Normalize)
  • Unstructured: Tokenize, Bag of Words
61
Q

Tokenization (Definition)

A

Data Preprocessing:

- Text -> Key words

62
Q

Document Term Matrix (Type)

A

Rows: Text Words
Columns: Words to be Analyzed (token defined previously)

63
Q

Bag of Words (Definition)

A
  • Created after data is cleansed and structured

- Pack of words

64
Q

Data Exploration (Types)

A
  • Structured:
  • Data Visualize
  • Feature Selection
  • Engineering OHE (convert classification into dummy)
  • Unstructured:
  • Feature Selection: word counts, frequency, cloud
  • Engineering: number length, N-gram (multi-word pattern), name entity recognition, part of speech
65
Q

Big Data Properties

A
  1. Variety (↑): Níveis de estrutura
  2. Velocity (↑): Latência
  3. Volume (↑): Terabytes
  4. Veracity (↓): fake news
66
Q

Order of Model Training Table

A

P (Vertical): 1 / 0
A (Horizontal): 1/0

Lembrar: Paulo Amora

H0 = class = 0
Ha = class ≠ 0 (ou seja, 1)
67
Q

Precision (Formula)

A

Precision (→): TP / (TP + FP)

Error #1 is bad

68
Q

Recall / Sensitivity (Formula)

A

Recall (↓): TP / (TP+FN)
Error #2 is bad
HIV = Não rejeitar H0, H0 false

69
Q

Accuracy (Formula)

A

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

All True / All Possibilities

70
Q

Receiver Operating Characteristic (ROC)

A

Chart about all POSITIVES (+)

X-axis: FPR = FP / (FP + TN exact opposite)
Y-axis: TPR = TP / (TP + FN exact opposite)

Highest area under chart = better

CFA L2 Matheus (9 decks)

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