Time series

1.A price is a random walk with no drift. A one-step forecast of the next price, given the price now, is what?

2.The same random walk is differenced. The differences are white noise. What does the variance of the price level do as time moves forward from a fixed start?

3.An AR(1) has coefficient 0.5 and a mean-zero shock. A shock of size 4 hits today. How large is its expected imprint one step later?

4.For that same AR(1) with coefficient 0.5, how many steps does it take for a shock's expected imprint to halve?

5.An AR(1) coefficient is estimated at 1.2. What does that say about a stationary model for the level?

6.An AR(1) coefficient is −0.6. Successive expected responses to a shock do what?

7.White noise is differenced by mistake. The lag-1 autocorrelation of the differenced series is what?

8.A moving-average process of order 1 has coefficient 0.5. Its autocorrelation is nonzero at which lags, beyond lag 0?

9.That MA(1) coefficient is 2, which sits outside [−1, 1]. An invertible representation with the same autocorrelation uses which coefficient?

10.Two independent random walks are regressed on each other over a long sample. A large t-stat on the slope is evidence of what?

11.Two random walks have a spread, price A minus 2 times price B, that is stationary and mean-reverting. What is that property called?

12.The spread in that cointegrated pair is high today. An error-correction model says the next change in the spread tends to do what?

13.Returns on a liquid name are approximately uncorrelated, but squared returns are strongly autocorrelated. What does that pair of facts point to?

14.A series of daily returns passes a test for no autocorrelation and fails a test on the autocorrelation of squares. Are the returns independent?

15.A deterministic linear trend is fitted to a pure random walk with no drift, and the residual is treated as the cycle. What is that cycle?

16.An augmented Dickey-Fuller test is not rejected. What does the null of that test say?

17.A KPSS test is not rejected. What does the null of that test say?

18.A price quotes at the bid or the ask with equal chance, and the efficient price is constant. The change in the observed quote has what lag-1 autocorrelation?

19.One name trades every minute and another trades every ten minutes, and both are driven by the same intraday news. A cross-correlation shows the frequent name leading the sparse one. What can create that lead without the frequent name containing extra news?

20.An Ornstein-Uhlenbeck process is sampled at a fixed time step. The sampled series is what?

21.A one-year forecast of a stationary AR(1) and a one-year forecast of a random walk are compared. As the horizon grows, the forecast-error variance does what in each case?

22.The impulse response of a random walk to a unit shock, at every horizon, is what?

23.Granger causality from X to Y means what?

24.A VAR of two returns is hit with a shock, and the researcher reports an impulse response without saying how the two shocks were separated. What is missing?

25.A seasonal difference is applied to a series that has a stable day-of-week mean and is otherwise white noise. The differenced series will show what?

26.Forecasts from two models are compared on overlapping multi-day returns. The loss differential is strongly autocorrelated. A test that treats each day as independent will do what to its standard error?

27.A researcher picks the AR lag length that minimizes the in-sample residual variance, with no penalty for extra lags. What lag length does that rule favor?

28.The autocorrelation of a stationary series dies quickly, but a mean shift halfway through the sample is ignored. The sample autocorrelation then looks like what?

29.Realized variance sums squared intraday returns. Microstructure noise in those returns does what to the sum as the sampling gets finer?

30.A hedge ratio is estimated by regressing price levels of two cointegrated names. A second ratio is estimated by regressing their returns. When are these ratios answering the same question?

31.The partial autocorrelation of an AR(2) cuts off after which lag?

32.The ordinary autocorrelation of a stationary AR(2) does what?

33.A series is already stationary. A colleague differences it once more before fitting an AR. The extra difference does what?

34.Forecasts of a stationary series, from the correct conditional mean, have errors that should be unpredictable from the information used in the forecast. A leftover lag-1 autocorrelation in those errors means what?

35.Two forecasts of the same return are combined with weights that sum to 1. The second forecast adds nothing if its error relative to the first is uncorrelated with the second forecast. That situation is called what?

36.A random walk with drift mu has a one-step forecast equal to what?

37.Daily closes are summed into a weekly price change by adding five daily random-walk increments. The weekly series is what?

38.A high-frequency cycle is sampled too slowly, below its Nyquist rate. The slow sample shows what?

39.The sample autocorrelation of a short series is biased toward zero at long lags partly because of what?

40.A researcher standardizes a series by its full-sample mean and variance, then studies the autocorrelation of the standardized series as if the mean and variance had been known in advance. For a series with a drifting variance, that standardization does what?

41.The Durbin-Watson statistic near 0, for residuals of a regression in time order, indicates what?

42.A regression of a return on its own lag uses ordinary least squares, and the errors are heteroskedastic. The slope point estimate is still consistent under standard conditions. The usual OLS standard error is what?

43.Newey-West standard errors are used on a regression with overlapping 10-day returns as the outcome. The lag window in the estimator is set to 0. What does that choice do?

44.A series has a unit root, and a regression includes both a constant and a linear time trend in the Dickey-Fuller specification even though the truth has neither. What is the main cost?

45.The half-life of an AR(1) with coefficient 0.9, in steps, is about what?

46.A researcher reports the autocorrelation of prices and the autocorrelation of returns for the same name. Which pattern is the ordinary one for a near-random-walk price?

47.A seasonal AR model puts the seasonal coefficient on the lag of 5 for a week of trading days. A shock's imprint at lag 5 is the seasonal coefficient. A shock's imprint at lag 1, if the nonseasonal coefficient is zero, is what?

48.A filter that takes a two-sided moving average of white noise is applied, and the smoothed series is then described as a cycle. What produced the wiggles?

49.An expanding-window forecast uses only data before each date. A rolling window of fixed length does the same if it ends at the forecast date. Which window forgets the distant past?

50.A multi-step forecast is made by iterating a one-step model, feeding forecasts back in. A direct multi-step regression predicts the h-day outcome from today's information in one equation. These match when what is true?

51.The innovation of a forecast is the one-step error. For the conditional mean of a series with finite variance, those innovations, under a correct model, are what?

52.A price is integrated of order 1, written I(1). Its return is integrated of order what, if the return has no further unit root?

53.A series is I(2). How many differences does it take to reach a stationary series?

54.Cointegration of two I(1) prices implies their cointegrating residual is I(0). It does not imply what?

55.The Engle-Granger regression estimates a cointegrating vector by least squares of one I(1) series on another, then tests the residual for a unit root. A failure to reject a unit root in the residual means what, at the usual size?

56.In a GARCH(1,1), a large squared shock today raises the forecast of tomorrow's variance. If both GARCH coefficients are positive and their sum is 0.95, that extra variance dies how?

57.An IGARCH model sets that sum to 1. A shock to variance then has a forecast imprint that does what as the horizon grows?

58.A realized-volatility series is itself persistent, and a researcher fits an AR(1) to it. The coefficient is 0.8. This describes persistence of what?

59.A structural break in the mean is dated after looking at the same series that will be used to test the break. The p-value from a test that pretends the date was fixed in advance is what?

60.A calendar dummy for each weekday is fitted, and the researcher then quotes the weekday means from that same fit as a discovered seasonal pattern, with no later sample. Those means are what?

61.The spectral density of white noise is what shape?

62.A series with a strong slow cycle has a spectral density that is large at which frequencies?

63.Prewhitening a series before computing a cross-correlation is done so that what does not dominate the picture?

64.A lead-lag regression of two return series uses contemporaneous and lagged terms, and the contemporaneous coefficient is the only large one. For a decision that must be made before either return is known, that coefficient is what?

65.The variance ratio of a q-period return to q times the one-period variance equals 1 for every q when the returns are uncorrelated. A variance ratio below 1 at long q points to what?

66.A variance ratio above 1 at a multi-week horizon, for a series of daily returns, points to what?

67.A local-level model says the observed series is a random walk plus independent measurement noise. The filtered estimate of the level is what, relative to the latest observation?

68.That same local-level filter is run with the measurement-noise variance set to zero. The filtered level equals what?

69.A researcher differences a price, fits a model, and forecasts the next difference. To forecast the price, they add that forecast to today's price. This is valid when what holds?

70.The same addition is done using a difference that was computed with a future price inside a centered smoother. The resulting price forecast is what?

71.A series of overlapping 5-day sums of a white-noise daily return has autocorrelation at lag 1 equal to what, approximately, ignoring edge effects?

72.Those overlapping sums are treated as the primitive series, and a t-stat pretends there is one independent observation per day. Relative to a t-stat on non-overlapping weeks, this t-stat is what?

73.A log price is a random walk, so the log return is white noise. The simple return, exp(log return) minus 1, is then what?

74.The expected simple return is 0.01 and the expected log return is −0.02. A forecast that compounds the expected log return describes what?

75.A researcher tests the autocorrelation of returns at lags 1 through 20 and highlights the one lag that is significant at 5 percent. Under a true white noise, the chance that at least one of 20 independent tests fails is about what?

76.The Ljung-Box test pools autocorrelations at several lags into one statistic. Compared with highlighting the largest single lag after looking at all of them, the pooled test does what?

77.A price and a dividend are both I(1), and the dividend yield is stationary. What does that say about the price and the dividend?

78.The cross-correlation from an index futures return to the cash index return is large and positive at lag 0 and also positive at a short positive lag from futures to cash. A trader who cannot deal in the cash print until after it is published can use which piece?

79.A state-space model writes a return as a latent mean plus noise, and the latent mean is an AR(1). If the AR coefficient of the latent mean is estimated at 0, the model collapses to what?

80.The same latent-mean model is estimated, and the filtered mean is plotted through the whole sample using the smoother, which uses future returns. Using that smoothed mean as a signal known on each past date does what?

81.A regression of the change in a spread on the lagged spread has a slope of −0.3, with a standard error that puts it well below zero. For a cointegrated spread, that sign is what?

82.That slope of −0.3 is the only regressor, and the spread was scaled to have variance 1. A one-standard-deviation high spread forecasts a next change of about what?

83.A researcher differences the spread of a cointegrated pair and then refuses to include the lagged level in the model for the changes. What has been thrown out?

84.Returns are uncorrelated, and their absolute values are autocorrelated. A mean forecast that uses only lagged returns, and ignores volatility, is missing what?

85.A long-memory estimate of the return's autocorrelation decays as a power of the lag rather than geometrically. A single mean break in an otherwise short-memory series can imitate that decay in a finite sample. A researcher who quotes the power as a stable memory parameter, without checking for a break, has not separated what?

86.The first difference of a series has an autocorrelation of −0.5 at lag 1 and about 0 after that. A plausible description of the original series is what?

87.A model for a positive volume series is fitted to log volume, and the forecast of log volume is exponentiated to forecast volume. That exponentiated forecast estimates what?

88.A researcher winsorises a return series at fixed percentiles of the whole sample, then estimates an AR(1) on the winsorised series. The early AR residuals depend on what?

89.Two volatility proxies, a squared return and a high-low range, are combined. The range is a more efficient scale estimator than the squared close-to-close return under a Brownian move. Using only the close-to-close square, and ignoring the range when it was observed, does what?

90.A forecast combination puts weight 1.4 on one model and −0.4 on another. What is a fair reading of the negative weight?

91.The same combination is constrained to nonnegative weights that sum to 1, and the unconstrained optimum wanted a negative weight. The constraint does what?

92.A series is observed with a missing day in the middle, and the gap is filled by linear interpolation before an AR(1) is fitted. The interpolated point is what kind of observation for the AR?

93.A trading clock drops overnight hours, and a calendar clock keeps them. An AR fitted on the trading clock assigns lag 1 to the previous trade, which may be yesterday's close relative to today's open. That lag is what?

94.The score of a correct conditional density, the log score, is proper. A researcher instead picks the model with the highest in-sample R-squared of the mean and ignores a density forecast. For a decision that depends on the whole distribution, that selection does what?

95.A model's one-step predictive density is transformed by the probability integral transform on a later sample, and the transforms pile up at both ends. The density was what?

96.Those transforms pile up near one half. The predictive density was what?

97.A researcher estimates an ARMA model by maximum likelihood and then simulates paths from it to judge a strategy, using the same sample the model was fitted on to judge the fit of the paths. Those paths check what?

98.The shock distribution used in that simulation is Gaussian, and the historical returns have a much fatter tail. Paths of a mean-reverting strategy's maximum loss will tend to do what, relative to history?

99.A bootstrap of a return series resamples single days independently. The historical series has volatility clustering. The bootstrap paths will do what to that clustering?

100.A block bootstrap draws contiguous weeks and concatenates them. Compared with the independent-day bootstrap, it is aimed at what?

101.The stationary bootstrap uses random block lengths with a fixed mean. A mean block length of one day reduces it to what?

102.A researcher reports a Sharpe ratio computed from a model-simulated path whose shocks were drawn from the fitted residuals of the same path's mean model, with no held-out period. Calling that Sharpe out of sample confuses what?

103.Simple exponential smoothing of a level, with no trend, is the same recursion as which model class?

104.A forecast of the mean is unbiased, and its error variance is large. A second forecast is slightly biased and much tighter. On squared error, the second can win. What is being traded?

105.An ARCH(1) sets today's variance equal to a constant plus a coefficient times yesterday's squared return. It does not include what, which a GARCH(1,1) adds?

106.The unconditional variance of a stationary GARCH(1,1) exists when the sum of the two slope coefficients is below 1. If a fit reports a sum of 1.05, what is wrong with quoting a long-run variance from the usual formula?

107.A researcher aligns a macroeconomic announcement to the daily close of the same calendar date, and the announcement is at 8:30 in the morning. The close is after the announcement. Using that close-to-close return as the outcome and the announcement surprise as a lag known before the close is what?

108.The same surprise is paired with the previous close-to-close return, the one that ended before 8:30. That pairing claims the market moved in response to a number that had not been released. What is the timing error?