Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates

Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation

Component-smoothed Inflation: Estimating the Persistent Component of Inflation in Real Time

This paper presents a new measure of underlying inflation: component-smoothed inflation. It approaches the problem of determining underlying inflation from a different direction than previous methods. Rather than excluding or trimming out volatile CPI items, it smoothes components of the CPI based on their volatility – CPI expenditure weights are maintained for all items. Items such as rent are smoothed a little, if at all, while volatile series such as fruit, vegetables and automotive fuel are smoothed a lot. This removes much of the temporary volatility in the CPI while retaining most of the persistent signal. Because our underlying inflation measure includes all CPI items at all times, it is robust to sustained relative price changes and is unbiased in the long run. A potential cost of this approach is that, unlike other measures, it places weight on lagged as well as contemporaneous prices for volatile series. An evaluation of the balance between the costs and benefits of this approach remains an open question.CPI; core inflation; underlying inflation; Australia; United States

Detecting and tracking time-varying causality with applications to EEG data

This paper introduces a novel method called the ERR-Causality, or Error Reduction Ratio Causality test, that can be used to detect and track causal relationships between two signals using a new adaptive forward orthogonal least squares (Adaptive-Forward-OLS) algorithm. In comparison to the traditional Granger method, one advantage of the new ERR-Causality test is that it can effectively detect the time-varying direction of linear or nonlinear causality between two signals without fitting a complete model. Another important advantage is that the ERR-Causality test can detect both the direction of interactions and estimate the relative time shift between the two signals. Several numerical examples are provided to illustrate the effectiveness of the new method for causal relationship detection between two signals. An important real application, relating to the analysis of the causality of EEG signals from different cortical sites which can be very useful for understanding brain activity during an epileptic seizure by inspecting the high-resolution time varying directed information flow, is also discussed

Cram\'er-Rao Bounds for Polynomial Signal Estimation using Sensors with AR(1) Drift

We seek to characterize the estimation performance of a sensor network where the individual sensors exhibit the phenomenon of drift, i.e., a gradual change of the bias. Though estimation in the presence of random errors has been extensively studied in the literature, the loss of estimation performance due to systematic errors like drift have rarely been looked into. In this paper, we derive closed-form Fisher Information matrix and subsequently Cram\'er-Rao bounds (upto reasonable approximation) for the estimation accuracy of drift-corrupted signals. We assume a polynomial time-series as the representative signal and an autoregressive process model for the drift. When the Markov parameter for drift \rho<1, we show that the first-order effect of drift is asymptotically equivalent to scaling the measurement noise by an appropriate factor. For \rho=1, i.e., when the drift is non-stationary, we show that the constant part of a signal can only be estimated inconsistently (non-zero asymptotic variance). Practical usage of the results are demonstrated through the analysis of 1) networks with multiple sensors and 2) bandwidth limited networks communicating only quantized observations.Comment: 14 pages, 6 figures, This paper will appear in the Oct/Nov 2012 issue of IEEE Transactions on Signal Processin

Noisy Fiscal Policy

This paper investigates the macroeconomic effects of fiscal policy in a setting in which private agents receive noisy signals about future shocks to government expenditures. We show how to empirically identify the relative weight of news and noise shocks to government spending and compute the level of noise for Canada, the UK and the US.We then investigate the quantitative implications of imperfect fiscal policy information using a medium-scale DSGE model. We find that when the government seeks to implement a persistent change in expected public spending, the existence of noise (as estimated using actual data) implies a sizable difference in fiscal multipliers compared to the perfect fiscal foresight case

Noisy Fiscal Policy

This paper investigates the macroeconomic effects of fiscal policy in a setting in which private agents receive noisy signals about future shocks to government expenditures. We show how to empirically identify the relative weight of news and noise shocks to government spending and compute the level of noise for Canada, the UK and the US.We then investigate the quantitative implications of imperfect fiscal policy information using a medium-scale DSGE model. We find that when the government seeks to implement a persistent change in expected public spending, the existence of noise (as estimated using actual data) implies a sizable difference in fiscal multipliers compared to the perfect fiscal foresight case