In the Roll model trade prices are pt = mt + cdt where mt is the efficient price (mid-price) and dt = 1 is the trade sign (indicator) which shows if the trade is a buy or sell.
The simple Roll model assumes that trade signs are serially uncorrelated: corr(dt, ds) = 0 for t ?= s. In practice, trade signs are correlated, with positive autocorrelation. Suppose that corr(dt, dt?1) = ? > 0 and corr(dt, dt?k) = 0 for k > 1. Suppose that ? > 0 is known. Also, assume that the trade signs dt are uncorrelated with the increments of the efficient price ?mt = ut.
i) Show that V ar(?pt) = 2c2(1 ? ?) + ?u2, Cov(?pt, ?pt?1) = ?c2(1 ? 2?), Cov(?pt, ?pt?2) = ?c2?, and Cov(?pt, ?pt?k) = 0 for k > 2.
ii) Suppose that 0
Hints. For (i), recall the corresponding expressions in the simple Roll 222
model V ar(?pt) = 2c + ?u and Cov(?pt, ?pt?1) = ?c .
Note that the equations above in (i) reduce to these expressions if ? = 0. Repeat the computations for the simple model allowing for the correlation ? and you should get the results stated.
37. You are given the following complete trial balance: Loitering Credits Account A $ 536 Account B Account C 332 Account D Account E ideal MeanA of libero 008. $1,044 Account Fed bedalumwood of Jidab: 0958 ac 322 Account G 218 Account H 894 awaiver ed blourie comethe $2,042 $2,478 A Which account appears to have its balance improperly transferred to the trial balance? a. Account A e. Account E b. Account B f. Account F c. Account C g Account G d. Account D h. Account Ha 38. You are given the following complete trial balance with one account con- taining a transposition error: Account A $ 354 Account B 422 Account C 1,073 Account D 365 Account E $ 725 Account F 993 Account G 629 Account H 137 $2,214 $2,484 Which account appears to contain the transposition error? a. Account A e. Account E b. Account B f. Account F c. Account C g. Account G de Account D h. Account H25. Consider a bivariate data set. We have: N, Mean, SD for both x and for y. With only these descriptive statistics, Pearson r a. can be calculated if N is large b. can be roughly estimated c. can be calculated d. cannot be calculated e. none of the above 26. Note that this is "an empirical question" that can be probed by a call to a power function from package "pwr". How will using a one-sided statistical test of correlation, rather than a two-sided test, impact statistical power, all other factors being equal? a. it will not influence statistical power b. it will increase statistical power c. it depends on alpha d. it depends on the size of r e. it depends on sample size f. it will decrease statistical power g. it depends on the desired level of significance h. none of the above 27. It is common for Pearson correlation to be statistically significant when a. sample size is large b. each variable is a "random variable" c. the Pearson assumptions are not met d. the data were measured with great error e. sample size is small f. the data are not bivariately normal 4. the Pearson assumptions are met h. the data are nonlinear i. none of the above 28. Reflecting modern statistical thought, which of the following is the proper way for correlation to be reported in a paper submitted to a peer-review scientific journal. a. p = 0.072, r = 0.55 b. r 0.05 d. r = 0.55, p = 0.072 e. none of the above29. Comprehensive, correlation analysis is performed weekly on a biomedical x, y data set with a large sample size of N > 2c6 that increases weekly by Al input of data from on-line medical records and from sensor feeds of wearable devices, e.g., implants, smart watches, Pearson r remains significant, as performed weekly, yet the magnitude of Pearson r fluctuates greatly. And, graphical visualization of scatter plots is frustrating due to over-plotting of points which makes dense "ink" blobs across the graphs. The analysts decide to apply a lowess fit each week to the ever growing scatter plots. Statistically, why the lowess fit? 3, as EDA b. to detect nonlinear trends C. to guide the eye d. to detect clusters e. to detect x, y "features" f. to assess linearity g. to explore the x, y data h. all the above 30. Consider this code chunk entered at the R Console. The LAST LINE of R code below, returns 3 rl 12 plot (rl, r2) I scatter plot cor. test (rl, r2, conf. level=. 99) a. Pearson r with two-sided significance test and 99% Cl of r b. Pearson r with two-sided significance test and 95% Cl of r c. Spearman r with one-sided significance test d. Pearson r with one-sided significance test and 99% Cl of r e. Spearman r with two-sided significance test f. Pearson r with one-sided significance test and 95% Cl of r 4- none of the above 31. The x, y data encoded in R below, is suitable for correlation analysis. Which of the following is both statistically accurate and written in the best format for reporting in a research paper. > x
