Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 6.09% per annum.
- PEP price at the close of May 2, 2024 was $175.45 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 9.36% per annum.
- PEP price at the close of May 2, 2024 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 PEP 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 24, 2022
End date: April 23, 2024
a = 5.4350
b = -0.0002
s = 0.0393
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -6.09%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0393) – 1
= 17.03%
October 24, 2022 calculations
Top border of price channel:
Exp(Y876)
= Exp(a + b × X876 + 2 × s)
= Exp(a + b × 1,270 + 2 × s)
= Exp(5.4350 + -0.0002 × 1,270 + 2 × 0.0393)
= Exp(5.2950)
= $199.33
Bottom border of price channel:
Exp(Y876)
= Exp(a + b × X876 – 2 × s)
= Exp(a + b × 1,270 – 2 × s)
= Exp(5.4350 + -0.0002 × 1,270 – 2 × 0.0393)
= Exp(5.1377)
= $170.33
April 23, 2024 calculations
Top border of price channel:
Exp(Y1,251)
= Exp(a + b × X1,251 + 2 × s)
= Exp(a + b × 1,817 + 2 × s)
= Exp(5.4350 + -0.0002 × 1,817 + 2 × 0.0393)
= Exp(5.2008)
= $181.42
Bottom border of price channel:
Exp(Y1,251)
= Exp(a + b × X1,251 – 2 × s)
= Exp(a + b × 1,817 – 2 × s)
= Exp(5.4350 + -0.0002 × 1,817 – 2 × 0.0393)
= Exp(5.0435)
= $155.02
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 6.09% per annum.
- PEP price at the close of May 2, 2024 was $175.45 and was inside the primary price channel.
Secondary Trend
Start date: October 5, 2023
End date: May 2, 2024
a = 4.7009
b = 0.0002
s = 0.0180
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 9.36%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0180) – 1
= 7.47%
October 5, 2023 calculations
Top border of price channel:
Exp(Y1,114)
= Exp(a + b × X1,114 + 2 × s)
= Exp(a + b × 1,616 + 2 × s)
= Exp(4.7009 + 0.0002 × 1,616 + 2 × 0.0180)
= Exp(5.1331)
= $169.54
Bottom border of price channel:
Exp(Y1,114)
= Exp(a + b × X1,114 – 2 × s)
= Exp(a + b × 1,616 – 2 × s)
= Exp(4.7009 + 0.0002 × 1,616 – 2 × 0.0180)
= Exp(5.0611)
= $157.76
May 2, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.7009 + 0.0002 × 1,826 + 2 × 0.0180)
= Exp(5.1846)
= $178.49
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.7009 + 0.0002 × 1,826 – 2 × 0.0180)
= Exp(5.1125)
= $166.09
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 9.36% per annum.
- PEP price at the close of May 2, 2024 was inside the secondary price channel.
- 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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