SS 3. Quantitative Methods: Application Flashcards
1 - the probability of a Type II error is:
The power of test
The p-value approach is:
The smallest level of significance at which the null hypothesis can be rejected
A t-distribution has (fatter/thinner) tails than a normal distribution
Fatter (because the t-distribution has a standard deviation greater than 1)
99% probability that any sample mean obtained is within ____ standard errors of the population mean
Two sided: 2.58
One sided: 2.33
What is the major difference when using technical analysis for the bond market compared to equities?
Trading volume for bonds is harder to obtain
90% probability that any sample mean obtained is within ____ standard errors of the population mean
Two sided: 1.645
One sided: 1.28
An uptrend line can be constructed by drawing a line that connects the:
lows of a price chart
When the sample data is dependent, we need to use what kind of test?
A paired comparison test
If population standard deviation is NOT KNOWN:
Standard Error =
SAMPLE standard deviation
/
square root of n (sample size)
A downtrend line can be constructed by drawing a line that connects the:
Highs of the price chart
The sampling distribution of the sampling mean is:
the distribution of the means of all possible samples of a given size from a given population
Type I Error:
Rejects a true hypothesis
The hypothesis accepted when null hypothesis is rejected is the:
alternative hypothesis
What are the formal steps in hypothesis testing? (7)
- Stating the null hypothesis and the alternative hypothesis
- Identifying the appropriate test statistic and its probability distribution
- Specifying the significance level
- Stating the decision rule
- Collecting the data and calculating the test statistic
- Making the statistical decision
- Making the economic or investment decision
‘Observations that represent a characteristic of individuals, groups, geographical regions, or companies at a single point in time’ describes:
Cross sectional data
The general target price for a ‘head and shoulders’ pattern is:
The neckline minus the amplitude of the head over the neckline
Test statistic =
(sample statistic - hypothesised value)
/
standard error of the sample statistic
Test statistic for F-distribution:
F = s1^2 / s2^2 (larger/smaller)
s^2 = sample variance
Define ‘Sampling Error’:
The difference between the observed value of a statistic and the quantity it is supposed to estimate
The short interest ratio =
the amount of short interest
/
average daily volume
The major cycles under Elliot Wave Theory are (9):
Grand supercycle supercycle cycle primary intermediate minor minute minuette subminuette
An estimator is:
a formula to calculate sample statistics
A sequence of data occuring at discrete and uniformly-spaced intervals is called:
a time series
Tracking risk is defined as:
The standard deviation of the difference between portfolio and benchmark returns
‘A formula to calculate sample statistics’ describes:
An estimator
A price range in which buying activity is sufficient to stop the decline in price of a security defines:
Support
For F-Test, the larger sample variance is placed on the:
numerator
Test statistic for Chi Squared distribution:
[(n-1) * sample variance]
/
Hypothesised variance
n-1 = degree of freedom
A company’s predicted stock price from an equity analysts model is a good example of:
A continuous random variable
A company’s predicted share price from a model could take on any value, thus is a continuous random variable. (note, a company’s share price on the stock exchange is limited to $0.01 movements, and is thus a discrete random variable).
The power of the test is:
1 - (probability of a Type II error)
Sampling from a database that only tracks companies currently in existence is an example of:
Sample selection bias (Survivorship bias)
As a technical analyst you are set the task of trying to identify intermarket relationships, what are you most likely to use to identify these relationships?
Relative Strength Analysis
The level of significance and the confidence level are:
Indirectly proportional
A common flow of funds indicator is the Arms Index, also called the TRIN. A value of less than 1 indicates:
There is more trading activity in rising stocks
1 - confidence level =
Probability of a Type 1 error
Sample mean - hypothesized mean
/
standard error
=
z-statistic
To standardize a random variable X, you should:
subtract the mean of X from X, then divide the result by the standard deviation of X
The power of test is the probability of:
rejecting the false null hypothesis
Name 3 Continuation patterns:
Triangle patterns
Rectangle patterns
Flags and pennants (minor continuation pattern)
What is the definition of retracement in the context of technical analysis?
The reversal in the movement of a security’s price such that it is counter to the prevailing longer-term price trend.
Doji:
A bar on a candlestick chart where the opening and closing price is the same.
Describe the Central Limit Theorem:
The population mean can be statistically described by the sample mean, as long as the sample size is large
If the level of confidence is lowered from 95% to 90%, but the allowable error and the standard deviation remain the same, what happens to the required sample size?
It decreases
A multivariate normal distribution is most likely to be defined by its constituents’ means, variances and:
Pairwise correlations
The t-distribution is used when the population variance is:
Unknown
How many pairwise return correlations does a 20 stock portfolio have?
190
20 choose 2
Formula for construction of confidence intervals:
Sample mean +/- z-score * Standard error
List the 5 biases in sampling that will cause an analyst’s conclusions to be in error:
- Data mining (or data snooping)
- Sample Selection
- Time Period Bias
- Look Ahead Bias
- Survivorship bias
95% probability that any sample mean obtained is within ____ standard errors of the population mean
Two sided: 1.96
One sided: 1.645
If sampling from a NONNORMAL distribution with an UNKNOWN variance, use a:
t-statistic or z-statistic (large sample size only)
What do we call the conditions under which the null hypothesis is not rejected?
Decision rule
The decision rule lays out the conditions under which we may compare the z values and decide whether or not to reject the hypothesis.
In the case of a test of the difference in means of two independent samples, we use a:
t-distributed statistic
Tracking error is defined as:
A portfolio’s gross return minus the benchmark return
Give 4 examples of Momentum Oscillators:
- Rate of change oscillator
- Relative strength index
- Stochastic oscillator
- Moving average convergence/divergence oscillator (MACD)
The probability of success of a Bernoulli random variable:
Stays the same with each trial
The trials are independent of each other
e.g. coin toss
The hypothesis to be tested is the:
null hypothesis
1 - significance level =
Degree of confidence
The distribution of all the distinct values a statistic can have when drawn form samples of the same size from the same population is the:
Sampling distribution
If sampling from a normal distribution with a KNOWN variance, use a:
z-statistic
The significance level of the test (alpha) is:
The probability of making a Type 1 error.
Identifying trading strategies by P/BV when BS is not available until later is an example of:
Look-ahead bias
Short time periods are likely to give results that may not reflect a longer time period
Long time periods are distortive if there has been a structural change
These are examples of:
Time-period bias
The _______ ______ _______ states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal, if the sample size is large enough
Central Limit Theroem
Type II Error:
Fails to reject a false hypothesis
The difference between statistic and estimated parameter (eg sample mean - population mean) is:
Sampling Error
A quantity from or describing a population (eg population mean) is a:
Parameter
A price range in which selling activity is sufficient to stop the rise in price of a security defines:
Resistance
In the test comparing variances of two normally distributed populations, we use:
An F-distributed test statistic
Technical traders tend to believe that the market is (efficient/not efficient)
Not efficient
To draw a downtrend line, the analyst has to draw a line that connects all the prior:
Highs of the trend period
If population standard deviation is KNOWN:
Standard Error =
POPULATION standard deviation
/
square root of n (sample size)
For F-Test, the larger sample variance is placed on the:
numerator
A function that determines the probability a random variable takes on a specific value is:
A probability function
E.g.
P(x) = x/5 if X = (1,2,3,4,5)
so
p(1) = 1/5 = 0.2
A 1-sample t-test uses a t-distribution with ____ degrees of freedom
n - 1
To standardise a random variable you are most likely to:
Subtract its mean from it and divide by one standard deviation
If sampling from a normal distribution with an UNKNOWN variance, use a:
t-statistic for small sample size
t-statistic or z-statistic for large sample size
What is it called when all the items in the population have the same chance of being selected for the sample?
Simple Random sampling
_____ sampling is a modified form of stratified random sampling used to reduce sampling costs when the population is scattered over a large geographic area.
Cluster sampling
The process of standardizing a normally distributed variable is:
Dividing the difference of mean and random variable by standard deviation.
If sampling from a NONNORMAL distribution with a KNOWN variance, use a:
z-statistic (large sample size only)
TRIN ratio =
(Number of advancing issues / number of declining issues)
/
(volume of advancing issues / volume of declining issues
The Kurtosis of a normal distribution is:
3
Statistical Inference is:
drawing conclusions about the entire population based on the statistical characteristics of a sample
A large sample size has at least:
30 observations
Drilling into data until you find something that appears to work is an example of:
Data-mining bias
Name 4 Reversal patterns:
Head and Shoulders
Inverse Head and Shoulders
Double tops and bottoms
Triple tops and bottoms
Give 2 examples of price-based indicators:
- Moving average
2. Bollinger bands
Chart patterns can be categorised into two main areas, namely:
Reversal and Continuation
In the context of technical analysis, the principle that states that ‘once a support level is breached, it becomes a resistance level’ is known as the:
change in polarity principle
‘One particular value that is used to estimate the underlying population parameter’ describes:
the point estimate
A distribution that explains the behavior of two or more dependent variables is referred to as:
A multivariate distribution
As n becomes large, t-distribution approaches:
normal distribution
A decrease in significance level reduces Type _ error, but increases chances of Type _ error
I, II
Name 3 situations when nonparametric tests are used:
When the data we use do not meet distributional assumptions
When the data are given in ranks
When the hypothesis we are addressing does not concern a parameter
Desirable properties of an estimator (3)
Unbiased
Efficient
Consistent
Elliott wave theory discusses how markets move. The key elements that R. N. Elliott proposes affect the way the market moves are in waves, that are described by:
Fibonacci ratios
