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 12.59% per annum.
- AAPL price at the close of November 19, 2024 was $228.28 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 78.17% per annum.
- AAPL price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $1.78 (0.78%). 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 AAPL 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: August 12, 2020
End date: June 10, 2024
a = 4.7067
b = 0.0003
s = 0.0868
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 12.59%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0868) – 1
= 41.53%
August 12, 2020 calculations
Top border of price channel:
Exp(Y182)
= Exp(a + b × X182 + 2 × s)
= Exp(a + b × 266 + 2 × s)
= Exp(4.7067 + 0.0003 × 266 + 2 × 0.0868)
= Exp(4.9668)
= $143.56
Bottom border of price channel:
Exp(Y182)
= Exp(a + b × X182 – 2 × s)
= Exp(a + b × 266 – 2 × s)
= Exp(4.7067 + 0.0003 × 266 – 2 × 0.0868)
= Exp(4.6195)
= $101.44
June 10, 2024 calculations
Top border of price channel:
Exp(Y1,144)
= Exp(a + b × X1,144 + 2 × s)
= Exp(a + b × 1,664 + 2 × s)
= Exp(4.7067 + 0.0003 × 1,664 + 2 × 0.0868)
= Exp(5.4211)
= $226.14
Bottom border of price channel:
Exp(Y1,144)
= Exp(a + b × X1,144 – 2 × s)
= Exp(a + b × 1,664 – 2 × s)
= Exp(4.7067 + 0.0003 × 1,664 – 2 × 0.0868)
= Exp(5.0738)
= $159.78
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 12.59% per annum.
- AAPL price at the close of November 19, 2024 was $228.28 and was inside the primary price channel.
Secondary Trend
Start date: March 1, 2024
End date: October 29, 2024
a = 2.6447
b = 0.0016
s = 0.0479
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0016) – 1
= 78.17%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0479) – 1
= 21.12%
March 1, 2024 calculations
Top border of price channel:
Exp(Y1,075)
= Exp(a + b × X1,075 + 2 × s)
= Exp(a + b × 1,563 + 2 × s)
= Exp(2.6447 + 0.0016 × 1,563 + 2 × 0.0479)
= Exp(5.2138)
= $183.80
Bottom border of price channel:
Exp(Y1,075)
= Exp(a + b × X1,075 – 2 × s)
= Exp(a + b × 1,563 – 2 × s)
= Exp(2.6447 + 0.0016 × 1,563 – 2 × 0.0479)
= Exp(5.0222)
= $151.74
October 29, 2024 calculations
Top border of price channel:
Exp(Y1,242)
= Exp(a + b × X1,242 + 2 × s)
= Exp(a + b × 1,805 + 2 × s)
= Exp(2.6447 + 0.0016 × 1,805 + 2 × 0.0479)
= Exp(5.5968)
= $269.55
Bottom border of price channel:
Exp(Y1,242)
= Exp(a + b × X1,242 – 2 × s)
= Exp(a + b × 1,805 – 2 × s)
= Exp(2.6447 + 0.0016 × 1,805 – 2 × 0.0479)
= Exp(5.4051)
= $222.54
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 78.17% per annum.
- AAPL price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $1.78 (0.78%). 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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