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 2.88% per annum.
- PG price at the close of April 26, 2024 was $161.29 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 11.65% per annum.
- PG price at the close of April 26, 2024 was inside the secondary price channel.
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 PG 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: July 23, 2021
End date: January 24, 2024
a = 4.8533
b = 0.0001
s = 0.0524
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 2.88%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0524) – 1
= 23.33%
July 23, 2021 calculations
Top border of price channel:
Exp(Y564)
= Exp(a + b × X564 + 2 × s)
= Exp(a + b × 816 + 2 × s)
= Exp(4.8533 + 0.0001 × 816 + 2 × 0.0524)
= Exp(5.0217)
= $151.67
Bottom border of price channel:
Exp(Y564)
= Exp(a + b × X564 – 2 × s)
= Exp(a + b × 816 – 2 × s)
= Exp(4.8533 + 0.0001 × 816 – 2 × 0.0524)
= Exp(4.8120)
= $122.98
January 24, 2024 calculations
Top border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 + 2 × s)
= Exp(a + b × 1,731 + 2 × s)
= Exp(4.8533 + 0.0001 × 1,731 + 2 × 0.0524)
= Exp(5.0930)
= $162.88
Bottom border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 – 2 × s)
= Exp(a + b × 1,731 – 2 × s)
= Exp(4.8533 + 0.0001 × 1,731 – 2 × 0.0524)
= Exp(4.8833)
= $132.06
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 2.88% per annum.
- PG price at the close of April 26, 2024 was $161.29 and was inside the primary price channel.
Secondary Trend
Start date: August 26, 2022
End date: April 26, 2024
a = 4.5149
b = 0.0003
s = 0.0403
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 11.65%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0403) – 1
= 17.49%
August 26, 2022 calculations
Top border of price channel:
Exp(Y840)
= Exp(a + b × X840 + 2 × s)
= Exp(a + b × 1,215 + 2 × s)
= Exp(4.5149 + 0.0003 × 1,215 + 2 × 0.0403)
= Exp(4.9624)
= $142.93
Bottom border of price channel:
Exp(Y840)
= Exp(a + b × X840 – 2 × s)
= Exp(a + b × 1,215 – 2 × s)
= Exp(4.5149 + 0.0003 × 1,215 – 2 × 0.0403)
= Exp(4.8012)
= $121.65
April 26, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.5149 + 0.0003 × 1,824 + 2 × 0.0403)
= Exp(5.1463)
= $171.79
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.5149 + 0.0003 × 1,824 – 2 × 0.0403)
= Exp(4.9851)
= $146.21
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 11.65% per annum.
- PG price at the close of April 26, 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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