# Publications

**High****F****requency****C****ovariance: A Julia Package for Estimating Covariance Matrices Using High Frequency Financial Data**** (with Margaryta Klymak), Journal of Sta****tisitical Software (forthcoming)**

High frequency data typically exhibit asynchronous trading and microstructure noise, which can bias the covariances estimated by standard estimators. While a number of specialised estimators have been proposed, they have had limited availability in open source software. HighFrequencyCovariance is the first Julia package which implements specialised estimators for volatility, correlation and covariance using high frequency financial data. It also implements complementary algorithms for matrix regularisation. This paper presents the issues associated with exploiting high frequency financial data and describes the volatility, covariance and regularisation algorithms that have been implemented. We then demonstrate the use of the package using foreign exchange market tick data to estimate the covariance of the exchange rates between different currencies. We also perform a Monte Carlo experiment, which shows the accuracy gains that are possible over simpler covariance estimation techniques.

**JEL Codes: ****C22, C58, G11, G12**** **

**Keywords: ****covariance estimation, correlation, volatility, high-frequency financial data, Julia**** **

**This was presented at JuliaCon 2021. The video is ****here****. The SSRN version of the paper is ****here****.**

**It's good to be bad: The lo****w quality advantage in consumer search markets**** **** (with ****Margaryta Klymak****), ****Economics Letters**** (2022), 2****15.**

The management and marketing literature has found that consumers generally expect high-quality sellers to post high prices. We show that low-quality firms can exploit this in search markets to generate a low price perception. This price perception can lead to low-quality firms dominating search markets while producing a vertically inferior good at equal cost to high-quality firms.â€‰

**JEL Codes: **D83, L15.

**Keywords: **Consumer search, Price perception, Quality

**Version as Edinburgh School of Economics discussion paper 280**

For a nontechnical explanation of this paper please press here

**Putting it off for later - Procrastination and end of fiscal year spending spikes****. ****The Scandinavian Journal of Economics (2019)****, 121 (2), pages 706-735.**

Many governments around the world exhibit heightened end of the fiscal year spending. These end of fiscal year spending spikes often concern policy makers due to their tendency to result in lower quality spending. This paper uses UK data to offer evidence against the precautionary savings explanation for spending spikes. An alternate explanation is offered with procrastination driving heightened end of fiscal year spending. A new technique of time variant budgetary taxes is calibrated to the model and shown to be effective for smoothing spending and improving spending efficiency throughout the fiscal year.

**JEL Codes: H11, H50, H61**

**Keywords: Government spending, fiscal year distortions**

For a nontechnical explanation of this paper please press here

**Fixed Point Acceleration in R**** (with ****Margaryta Klymak****),**** The R Journal**** (2019) 11(1), pages 359-375. **

A fixed point problem is one where we seek a vector X for a function f(x) such that f ( X ) = X . The solution of many such problems can be accelerated by using a fixed point acceleration algorithm. With the release of the FixedPoint package there is now a number of algorithms available in R that can be used for accelerating the finding of a fixed point of a function. These algorithms include Newton acceleration, Aitken acceleration and Anderson acceleration as well as epsilon extrapolation methods and minimal polynomial methods. This paper demonstrates the use of fixed point accelerators in solving numerical mathematics problems using the algorithms of the FixedPoint package as well as the squarem method of the SQUAREM package.