Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 0.82% per annum.
- MCD price at the close of November 19, 2024 was $290.73 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 83.26% per annum.
- MCD price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $16.23 (5.29%). This indicates a possible reversal in the secondary trend direction.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of MCD price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: October 27, 2022
End date: August 16, 2024
a = 5.5648
b = 0.0000
s = 0.0493
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 0.82%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0493) – 1
= 21.77%
October 27, 2022 calculations
Top border of price channel:
Exp(Y739)
= Exp(a + b × X739 + 2 × s)
= Exp(a + b × 1,072 + 2 × s)
= Exp(5.5648 + 0.0000 × 1,072 + 2 × 0.0493)
= Exp(5.6874)
= $295.11
Bottom border of price channel:
Exp(Y739)
= Exp(a + b × X739 – 2 × s)
= Exp(a + b × 1,072 – 2 × s)
= Exp(5.5648 + 0.0000 × 1,072 – 2 × 0.0493)
= Exp(5.4904)
= $242.34
August 16, 2024 calculations
Top border of price channel:
Exp(Y1,191)
= Exp(a + b × X1,191 + 2 × s)
= Exp(a + b × 1,731 + 2 × s)
= Exp(5.5648 + 0.0000 × 1,731 + 2 × 0.0493)
= Exp(5.7022)
= $299.51
Bottom border of price channel:
Exp(Y1,191)
= Exp(a + b × X1,191 – 2 × s)
= Exp(a + b × 1,731 – 2 × s)
= Exp(5.5648 + 0.0000 × 1,731 – 2 × 0.0493)
= Exp(5.5051)
= $245.95
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 0.82% per annum.
- MCD price at the close of November 19, 2024 was $290.73 and was inside the primary price channel.
Secondary Trend
Start date: May 23, 2024
End date: October 24, 2024
a = 2.7524
b = 0.0017
s = 0.0281
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0017) – 1
= 83.26%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0281) – 1
= 11.89%
May 23, 2024 calculations
Top border of price channel:
Exp(Y1,133)
= Exp(a + b × X1,133 + 2 × s)
= Exp(a + b × 1,646 + 2 × s)
= Exp(2.7524 + 0.0017 × 1,646 + 2 × 0.0281)
= Exp(5.5403)
= $254.76
Bottom border of price channel:
Exp(Y1,133)
= Exp(a + b × X1,133 – 2 × s)
= Exp(a + b × 1,646 – 2 × s)
= Exp(2.7524 + 0.0017 × 1,646 – 2 × 0.0281)
= Exp(5.4280)
= $227.69
October 24, 2024 calculations
Top border of price channel:
Exp(Y1,239)
= Exp(a + b × X1,239 + 2 × s)
= Exp(a + b × 1,800 + 2 × s)
= Exp(2.7524 + 0.0017 × 1,800 + 2 × 0.0281)
= Exp(5.7959)
= $328.95
Bottom border of price channel:
Exp(Y1,239)
= Exp(a + b × X1,239 – 2 × s)
= Exp(a + b × 1,800 – 2 × s)
= Exp(2.7524 + 0.0017 × 1,800 – 2 × 0.0281)
= Exp(5.6836)
= $294.00
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 83.26% per annum.
- MCD price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $16.23 (5.29%). This indicates a possible reversal in the secondary trend direction.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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