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 0.16% per annum.
- SYY price at the close of October 14, 2024 was $75.22 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.81% per annum.
- SYY price at the close of October 14, 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 SYY 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: February 22, 2021
End date: October 14, 2024
a = 4.3008
b = 0.0000
s = 0.0597
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= -0.16%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0597) – 1
= 26.96%
February 22, 2021 calculations
Top border of price channel:
Exp(Y340)
= Exp(a + b × X340 + 2 × s)
= Exp(a + b × 496 + 2 × s)
= Exp(4.3008 + 0.0000 × 496 + 2 × 0.0597)
= Exp(4.4180)
= $82.93
Bottom border of price channel:
Exp(Y340)
= Exp(a + b × X340 – 2 × s)
= Exp(a + b × 496 – 2 × s)
= Exp(4.3008 + 0.0000 × 496 – 2 × 0.0597)
= Exp(4.1793)
= $65.32
October 14, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.3008 + 0.0000 × 1,826 + 2 × 0.0597)
= Exp(4.4121)
= $82.45
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.3008 + 0.0000 × 1,826 – 2 × 0.0597)
= Exp(4.1734)
= $64.94
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 0.16% per annum.
- SYY price at the close of October 14, 2024 was $75.22 and was inside the primary price channel.
Secondary Trend
Start date: August 10, 2023
End date: October 14, 2024
a = 3.7497
b = 0.0003
s = 0.0527
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 12.81%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0527) – 1
= 23.46%
August 10, 2023 calculations
Top border of price channel:
Exp(Y961)
= Exp(a + b × X961 + 2 × s)
= Exp(a + b × 1,395 + 2 × s)
= Exp(3.7497 + 0.0003 × 1,395 + 2 × 0.0527)
= Exp(4.3158)
= $74.88
Bottom border of price channel:
Exp(Y961)
= Exp(a + b × X961 – 2 × s)
= Exp(a + b × 1,395 – 2 × s)
= Exp(3.7497 + 0.0003 × 1,395 – 2 × 0.0527)
= Exp(4.1051)
= $60.65
October 14, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.7497 + 0.0003 × 1,826 + 2 × 0.0527)
= Exp(4.4582)
= $86.33
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.7497 + 0.0003 × 1,826 – 2 × 0.0527)
= Exp(4.2474)
= $69.92
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.81% per annum.
- SYY price at the close of October 14, 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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