题目1836 · 统计
AR(1) Forecast Error Variance 1
For the AR(1) model X_t = phi X_(t-1) + e_t with phi = 0.6 and Var(e_t) = 1, what is the h = 3 step forecast error variance?
打开 →找到 30 个结果
中文题目题目1838 · 统计
AR(1) Forecast Error Variance 3
For the AR(1) model X_t = phi X_(t-1) + e_t with phi = 0.5 and Var(e_t) = 2.25, what is the h = 4 step forecast error variance?
打开 →题目1821 · 统计
AR(1) Multi-Step Forecast 1
A signal follows X_t = 0 + 0.6 X_(t-1) + e_t with Var(e_t) = 2 and current value X_t = 10. What is the h = 3 step forecast E[X_(t+3) | X_t]?
打开 →题目1822 · 统计
AR(1) Multi-Step Forecast 2
A signal follows X_t = 4 + 0.7 X_(t-1) + e_t with Var(e_t) = 1.5 and current value X_t = 8. What is the h = 2 step forecast E[X_(t+2) | X_t]?
打开 →题目1823 · 统计
AR(1) Multi-Step Forecast 3
A signal follows X_t = -1 + 0.8 X_(t-1) + e_t with Var(e_t) = 1 and current value X_t = 3. What is the h = 4 step forecast E[X_(t+4) | X_t]?
打开 →题目5181 · 金融与交易
Arbitrage Direction 1
Spot is 100, maturity is 1 years, and the funding rate is 0.03. The quoted forward price is 104. Assuming no income and no frictions, which arbitrage direction is indicated, and what is the mispricing per unit relative to fair value?
打开 →题目5182 · 金融与交易
Arbitrage Direction 2
Spot is 90, maturity is 0.5 years, and the funding rate is 0.04. The quoted forward price is 91. Assuming no income and no frictions, which arbitrage direction is indicated, and what is the mispricing per unit relative to fair value?
打开 →题目6026 · 统计
ARCH(1) as the Beta-Zero Special Case
A GARCH(1,1) reduces to ARCH(1) when $\beta=0$: $h_t=\omega+\alpha r_{t-1}^2$. With $\omega=0.7$ and $\alpha=0.3$, compute the unconditional variance $\bar h$ as a decimal.
打开 →题目1443 · 数学
Arcsine Cubic Remainder
Compute lim_{x->0} [arcsin x - x] / x^3.
打开 →题目3262 · 数学
Area of a Parallelogram from a Unit Square
The map $x=u+v,\ y=u-v$ sends the unit square $0\le u,v\le 1$ to a parallelogram. What is its area?
打开 →题目3265 · 数学
Area of a Polar Wedge
Use the polar Jacobian to compute the area of the region $0\le r\le 2,\ 0\le \theta\le \pi/3$.
打开 →题目3261 · 数学
Area of an Ellipse from the Unit Disk
The map $x=2u,\ y=3v$ sends the unit disk $u^2+v^2\le 1$ to an ellipse in the $(x,y)$-plane. What is the area of that ellipse?
打开 →题目3264 · 数学
Area Scaling Under a Triangular Map
The map $x=u,\ y=u+2v$ sends the unit square to a parallelogram. Compute the image area.
打开 →题目3966 · 金融与交易
Arithmetic-Average Call I
An arithmetic-average Asian call uses four equally weighted fixings. The first three fixings are [100, 102, 98], the strike is 100, and the desk wants the final payoff to be 4. What fourth fixing is required?
打开 →题目3968 · 金融与交易
Arithmetic-Average Call II
A weighted arithmetic-average Asian call uses weights [1, 1, 1, 2] on four fixings. The first three fixings are [50, 52, 51], the strike is 53, and the trader wants payoff 1. What final fixing is required?
打开 →题目3970 · 金融与交易
Arithmetic-Average Call III
An average-strike Asian call uses four equally weighted fixings including the terminal price. The first three fixings are [90, 94, 95]. What terminal price makes the payoff exactly 5?
打开 →题目3967 · 金融与交易
Arithmetic-Average Put I
An arithmetic-average Asian put uses four equally weighted fixings. The first three fixings are [80, 78, 82], the strike is 81, and the desk wants the final payoff to be 2.5. What fourth fixing is required?
打开 →题目3969 · 金融与交易
Arithmetic-Average Put II
A weighted arithmetic-average Asian put uses weights [1, 1, 1, 2]. The first three fixings are [40, 39, 42], the strike is 41, and the target payoff is 0.5. What final fixing is required?
打开 →题目1844 · 统计
ARMA Identification or Simplification 4
You observe the diagnostic statement: AIC prefers ARMA(2,1) but BIC prefers ARMA(1,1). What is the correct modeling conclusion?
打开 →题目5862 · 数理金融
Arrow-Debreu Prices From Option Quotes
A stock has three future states with prices 120, 100, and 80; the risk-free rate is 0. Calls struck at 80 trade at 28 and calls struck at 100 trade at 8. Using the digital/butterfly decomposition, find the Arrow-Debreu price of the single highest state (the state where the stock
打开 →题目1841 · 统计
ARMA Identification or Simplification 1
You observe the diagnostic statement: ACF tails off geometrically, PACF cuts after lag 1. What is the correct modeling conclusion?
打开 →题目1842 · 统计
ARMA Identification or Simplification 2
You observe the diagnostic statement: ACF cuts after lag 1, PACF tails off. What is the correct modeling conclusion?
打开 →题目1843 · 统计
ARMA Identification or Simplification 3
You observe the diagnostic statement: Both ACF and PACF tail off. What is the correct modeling conclusion?
打开 →题目1845 · 统计
ARMA Identification or Simplification 5
You observe the diagnostic statement: (1-0.5L) X_t = (1-0.5L) e_t. What is the correct modeling conclusion?
打开 →题目5857 · 数学
Arithmetico-Geometric Series
Evaluate the infinite series sum_(n=1)^inf n * (1/2)^n.
打开 →题目5827 · 金融与交易
A dealer faces order flow where a fraction 0.4 of traders ar
A dealer faces order flow where a fraction 0.4 of traders are informed (always trade in the correct direction) and 0.6 are noise traders who buy or sell with equal probability. The true value is equally likely high or low, so informed traders buy half the time and sell half the t
打开 →题目4115 · 金融与交易
A Fast Sanity Check for Risk-Parity Answers
What is a fast sanity check after you compute a risk-parity or inverse-vol allocation?
打开 →题目2867 · 概率
A Generalized Markov Bound from the Fourth Moment
Suppose $X$ is any random variable with $E[X^4]=81$. Use Markov's inequality on a suitable nonnegative variable to bound $P(|X|\ge 6)$.
打开 →题目2819 · 概率
A Generic Even-Parity Formula
Let $X$ be a nonnegative integer-valued random variable with PGF $G_X(s)$. Express $P(X\text{ is even})$ in terms of $G_X(-1)$.
打开 →题目6012 · 概率
A Three-Arrival Head Start
Aggressive and passive child orders fill as independent Poisson processes with rates $\lambda_A=10$ and $\lambda_B=5$ per minute. What is the probability that the first three fills in the merged stream are all aggressive (stream A)?
打开 →