7
votes
Estimate covariance matrix using prices
If you assume that a financial asset price has a change that is a wiener process then you can view the future value of that asset as the initial value plus the sum of the independent daily changes (...
- 9,195
6
votes
Are cumulative returns stationary?
Hi: Even if returns were stationary ( which is probably dependent on the time series one is considering ), cumulative returns, where $n$ is not fixed ( as it in say a rolling sum with a fixed window ...
- 1,082
5
votes
log return of sp500. Stationary vs strictly stationary
We can talk about whether a strictly stationary or weakly stationary process might usefully describe that data. My answer to both would be yes.
I also have issues with other text that people have ...
- 6,924
5
votes
Differencing vs Detrending financial time series
Hi: It depends on what the DGP of the original process is. Is the process trend stationary or difference stationary ? If it's trend stationary then de-trending is the way to go. If it's difference ...
- 1,082
4
votes
Accepted
Does predictability in a VAR process imply mean reversion or momentum?
The point of confusion may be in thinking that a predictable price process is synonymous with a mean-reverting process while using the definitions in these papers, it's actually the opposite! In the ...
- 6,924
4
votes
Are cumulative returns stationary?
Stock prices are definitely not stationary as tomorrows closing price is strongly influenced by today's closing price and prices tend to change. Returns can be potentially stationary and are therefore ...
- 8,438
3
votes
How to use autocorrelation plot to interpret time series data?
Just by looking at the graphs, I'd say:
Unit root
Constant series
Seasonality
AR model
No AC
No AC
- 707
3
votes
Issues making series stationary
Your shift is in the wrong direction.
Do this:
df.price = pd.to_numeric(df.price)
df['logret'] = np.log(df.price/df.price.shift(1))
- 750
3
votes
Accepted
Does Weak stationarity imply ergodicity ?
Ergodicity is connected to mixing, meaning there is one limiting distribution and it is used for time averages too. If you take a process in the real numbers that starts at a random value and then ...
- 240
3
votes
Accepted
Transforming a time series
Fractional differentiation (or differencing) is a technique that transforms an input series to a stationary series while retaining "long-term" memory.
Consider the following example based on ...
- 1,162
2
votes
Stationary Process with autocorrelation in Variance; square root rule
You are correct in that the series is not stationary. The ADF test isn't designed to test for stationarity outside the center of location. You are not going to be able to use the square root rule to ...
- 4,359
2
votes
Accepted
Would you consider yield a stationary or non-stationary process?
Following Meucci (Risk and Asset Allocation book, page 112-113) you should use "change of yield to maturity" (simple change, not percentage) since they represent Fixed Income´s invariant.
Change of ...
- 296
2
votes
Does forecasting asset returns by default assumes non-stationarity of asset returns?
This looks confused? I don't understand what you're saying in the second paragraph...
Comment 1: "Best" forecast depends on what you mean by "best."
Let $Y$ be a random variable and $\mathcal{F}$ be ...
- 6,924
2
votes
Accepted
Estimate covariance matrix using prices
For the same reason you can't meaningfully measure covariance/correlation using price of individual assets...correlation (covariance by extension) represents the comovement in deviations from ...
- 1,643
2
votes
Differencing vs Detrending financial time series
Let me try to write formulae to explain the differences:
When $X_t=a+b\,t + c\,\xi_t$, where $\xi_t$ is an iid centered and reduced noise (ie $\mathbb{E}\xi=0$ and $\mathbb{E}\xi^2=1$.
With $X_(t+1)-...
- 11.5k
2
votes
Accepted
Do stationary prices need to be differenced for VaR?
I worry that power prices are very unlikely to be stationary.
It is possible the mean does not vary wildly over time, and the price process may not be integrated, i.e. prices may not require ...
- 2,880
2
votes
Exchange rate trend-stationarity
Both @Con and @markleeds give good advice. Please don't worry - ADF is famously headache-inducing ;-)
The core problem here is that drifts and trends look horribly alike; and thus approaches like ADF ...
- 5,041
2
votes
Accepted
Are cumulative returns stationary?
In a nutshell...
It's always prudent and conservative to assume that prices are non-stationary.
But it's not actually as obvious this is true as it intuitively sounds. Intuitively, any random walk ...
- 5,041
1
vote
How to extract p-value from ur.df package of urca in R?
Using dput() you can inspect an R object, e.g.
dput(lc.df)
Using that I found that the p-values are stored in an attribute <...
- 8,438
1
vote
How to use autocorrelation plot to interpret time series data?
There is a multitude of texts which answer this question the easiest and free source is Rob Hyndmans from Monash Universities online text on forecasting, https://otexts.com/fpp2/, the topic is covered ...
- 304
1
vote
Exchange rate trend-stationarity
This is done simply in R with Rob Hyndmans Forecast packages, you need to run ACF, and PACF, there is an automatic algorithm for calculating the model of best fit, which takes most of the difficulty ...
- 304
1
vote
Accepted
How can I approximate Dollar Bars from Minute Data instead of Tick Data?
The following python package, mlfinlab, provides an implementation for both standard and information-driven bars. The good news is that you won't have to implement the techniques from scratch and they ...
- 924
1
vote
log return of sp500. Stationary vs strictly stationary
They probably can be modelled using a weakly stationary process.
To quote Section 1.2.1 from these lecture notes:
[Asset] returns [...] typically fluctuate around a constant level,
suggesting a ...
- 200
1
vote
Does forecasting asset returns by default assumes non-stationarity of asset returns?
If we assume the assets returns are stationary then the best forecast can only be the mean of the distribution.
This part is not accurate. Stationarity, even in its strongest sense, only implies that ...
- 113
1
vote
Accepted
principal component analysis on non stationary data
You may know that they are two definitions of stationary (see for instance Series of Irregular Observations: Forecasting and Model Building; this book probably contains all you need to model ...
- 11.5k
1
vote
Accepted
Real time stationarity test
We assume weak stationarity definition. Price level is non-stationary. Trend-stationarity is like following a trend, not working on this time scale. So need to use returns. Returns on interval <...
- 151
1
vote
Confusion on stationarity vs deterministic trend
Suppose the data generating process as your have suspected is as follows:
$$y_t = \gamma t + \epsilon_t$$
A first difference of the series will be
$$\Delta y_t = \gamma + \epsilon_t - \epsilon_{t-1}$$
...
- 650
1
vote
Accepted
ARIMA Forecasting always converges?
It is too much too text so I take screenshots and the link to Rob Hynman's blog entry:
If you formulate the ARIMA model likes this:
Then you get these long term forecasts:
- 13.6k
1
vote
Simulate non-stationary time series with cointegration
Simulate Random Walk Series
We can now simulate a random walk series in R as shown below:
RW <- arima.sim(model= list(order = c(0, 1, 0)), n=200)
We can plot the newly generated series as well ...
1
vote
Squared and Absolute Returns
Also, often we can assume the average of short-term returns in the long run to be zero, the historic volatility is equal to
$\hat{\sigma_T^2}=\frac{\sum_{i=1}^T{r_i^2}}{T-1}$. Sp to study the ...
- 177
Only top scored, non community-wiki answers of a minimum length are eligible